1.0 USING FEPC, FEPCIP, AND FEPCOPFEPC is a program that performs finite element stress analysis ofthree-dimensional truss, and twodimensional beam, plane solid, oraxisymmetric solid structures. There are two companion programs. FEPCIP is the FEPC INPUT PROCESSOR which is used to input and checka model and prepare data files for FEPC. FEPCOP is the FEPC OUTPUTPROCESSOR which reads FEPC output data files and produces graphicdisplays.The commercial version of the FEPC programs are currentlydimensioned to run in a PC with 640K memory. The dimension limitsin the programs are 600 nodes, 600 elements, 10 materials, 100points, 30 lines, and 20 arcs. Also, the overall model size islimited in FEPC based on number of nodes and average nodalbandwidth. For example, 600 nodes with an average nodal bandwidthof 15, 500 with 18, or 400 with 24 are all maximum model sizes thatcan be run in FEPC. Dimension limits of the automatic meshgeneration grid in FEPCIP are I=25 by J=60. Therefore a model canbe built in FEPCIP even within the 600 node and element limit whichis too large to run in FEPC, so plan carefully.The procedure for solving a problem is to run FEPCIP to create themodel, run FEPC to solve the equations, and run FEPCOP to displaythe results. The FEPCIP program presents the user with menus forinteractive input, checking and storing a model. This creates ananalysis file used as input for FEPC. Running FEPC produces alisting file of printout results and files of results used asinput for FEPCOP. Graphic displays of deformed shape and stressplots may then be produced by FEPCOP.0*((@@ 2.0 ENTERING THE MODEL IN FEPCIPBefore starting to enter the model, develop a node and elementnumbering plan, boundary conditions, and the load placement for themodel.With the FEPCIP.EXE file in the current drive and directory, beginby typing FEPCIPwhere means press the enter or return key. After the FEPCIPlogo appears the program will continue after a short pause.The screen will clear and the program will automatically detect theproper graphics mode for the supported graphics cards. Thesupported cards are IBM CGA, EGA, VGA, and MCGA of the PS/2 model30 along with the Hercules graphics card.After making the selection the main menu and graphics windows willthen appear along with a prompt to PICK A FUNCTION.INPUT PROCESSOR FINITE ELEMENT PERSONAL COMPUTER DATE TIMETITLE:+---------------++--------------------------++------------------+| || || ||F1 FILES || || MODEL ||F2 MODEL DATA || || SUMMARY ||F3 2D AUTOMSH || || WINDOW ||F4 TITLE || || || || |+------------------+| || |+------------------+| || MODEL || ||F6 CLEAR MEM || GRAPHICS || ||F7 EXIT || WINDOW || ||F8 VIEW OPTS || || ||F9 DSPLY OPTS || || || || || || || || ||PICK A || || ||FUNCTION || || || || || |+---------------++--------------------------++------------------+'0*((@@Selection of a menu item by tapping a function key brings up abranch menu.X Key F1 branches to a menu for recalling a previously storedmodel, storing a new model, or adding a title.(# X Key F2 branches to a menu for entering or editing all datarequired for the model.(# X Key F3 branches to a menu for two-dimensional area meshgeneration.(# X Key F4 prompts the user to input a title for the currentmodel.(# X Key F6 will clear all the current model data from memory inorder to start entering a new model.(# X Key F7 exits the program.(# X Key F8 branches to a menu to change the current view of themodel.(# X Key F9 branches to a menu to change the visibility of entities(nodes, elements, loads, etc.) or labels (node numbers,element numbers) on the next redraw of the model.(# Every branch menu has a function selection to return to theprevious menu. Many of the selections on the branch menus willbranch to additional menus. In each case, following completion oftasks on the current menu, use the previous menu selection to stepback through the menus until the modeling is complete.The general procedure for entering a model is to use the MODEL DATAfunction to access the menu for selecting the element type,defining the material properties, defining nodes and elements,setting node displacement restraints, and applying loads. Fortruss and beam element models all the model data are entered fromthis menu and its branch menus.Two-dimensional solid models using plane stress, plane strain, oraxisymmetric elements may first use the 2D AUTOMSH selection togenerate the model mesh of nodes and elements. Once the nodes andelements are defined return to the model data menu to complete themodel by material definition, setting node restraints and loads.The model must be stored on a disk file before exiting the program. The model data may be saved to disk at any time in the progress ofbuilding the model. Two files are stored for all complete modelsunder a user specified filename with file extensions of .MOD and.ANA. If the model is incomplete only the .MOD file is stored andmessages denoting the yet to be defined data for the .ANA file aredisplayed. All the current model data is saved in the .MOD file.The program operates by using the function keys to select theoperation from the menu. When data is required a prompt appears onthe data entry line just below the TITLE: header. The user typesin the requested data separated by commas or spaces followed bythe carriage return or enter key.' 0*((@@IF A MOUSE IS INSTALLED AND ITS DRIVER IS LOADED, THE MOUSE MAY BEUSED TO SELECT A MENU ITEM OR DETECT ENTITIES. MENU ITEMS MAY BESELECTED BY PRESSING THE CORRECT FUNCTION KEY OR BY POSITIONING THEMOUSE CURSOR OVER THE FUNCTION AND CLICKING THE LEFT BUTTON.WHEN THE PROMPT TO DETECT AN ENTITY APPEARS ON THE DATA ENTRY LINEA CURSOR WILL APPEAR IN THE MODEL GRAHPICS WINDOW. IF A MOUSEEXISTS AND ITS DRIVER IS LOADED THEN USE THE MOUSE TO POSITION THECURSOR AND CLICK THE LEFT BUTTON TO DETECT OR THE RIGHT BUTTON TOABORT. OTHERWISE WITHOUT A MOUSE USE THE ARROW KEYS TO POSITIONTHE CURSOR AT THE ENTITY LOCATION AND PRESS THE SPACE BAR TO DETECTOR PRESS THE RETURN OR ENTER KEY TO ABORT THE DETECT AND TERMINATETHE CURRENT OPERATION.2.1 FILESSelecting FILES from the main menu branches to the submenu below. +---------------+ | F1 RCL FN.MOD| | F2 STO FN.MOD| | & FN.ANA| | | | | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | | | +---------------+A previously formed and stored model may be recalled from disk byselecting F1 RCL FN.MOD. The user is prompted to enter thefilename, FN, without its .MOD extension. The filename mayinclude the drive designation and path, but it may be a maximum of20 characters long including the drive and path characters. DO NOTenter any leading blank spaces in the input of the filename. Ifthe file cannot be found an error message is displayed.The current model may be stored on disk by selecting F2 STO FN.MOD& FN.ANA. The model currently in memory will be stored in FN.MODassuming no errors. Also, if the model is complete and ready foranalysis the input file for the FEPC program will be stored inFN.ANA. If the model is incomplete the user is given messagesindicating which data are missing. The store operation may be doneat any time during the progressive construction of the model in'0*((@@order to have a place to restart in case of destruction of thecurrent model data in memory. If the files FN.MOD and FN.ANAalready exist on the disk they may be overwritten with the user'sconsent by the current data in memory each time the store functionis executed.After completing use of this branch menu select F10 PREV MENU toreturn to the main menu.2.2 MODEL DATABegin entering a new model by selecting F2 MODEL DATA on the FEPCIPmain menu. This produces the branch menu shown below. If a trussor beam element model is to be entered then all the model data willbe entered from this menu. If a two-dimensional solid is to beentered then all the data may be entered from this menu or the 2DAUTOMSH selection may be used to generate the nodes and elementsfor the mesh. Once these are generated they may be edited fromthis menu. If 2D AUTOMSH is to be used it should be done first orafter the element type is selected and material property sets aredefined since it will overwrite any existing node and elementdefinitions. +---------------+ | F1 ELEM TYPE | | F2 MATL PROP | | F3 NODE DEF | | F4 ELEM DEF | | F5 RESTRAINTS| | F6 LOADS | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | | | +---------------+ ` ` ELEMENT TYPEThis selection displays the list of available elements shown below. Use the indicated function key to select the element for the model. ' 0*((@@Only one element type may be used in a model. After selection theprogram returns to the previous menu. +---------------+ | F1 TRUSS | | F2 BEAM | | F3 PLN STRESS| | F4 PLN STRAIN| | F5 AXISYMMETR| | | | | | | | PICK A | | FUNCTION | | | +---------------+If the element type has been previously selected, then a promptdenotes that and requests the user's consent to change. Two nodetruss or beam elements may not be interchanged with any of thetwo-dimensional quadrilateral 4 node elements if any elements havebeen defined. 2D truss and beam elements may be interchangedprovided the material property sets are redefined and displacementboundary conditions are checked for validity. Plane stress, planestrain, or axisymmetric element types may be interchanged withoutany other data changes, but with obvious effects on the overallmodel behaviour. ` ` MATERIAL PROPERTIESThis selection branches to the menu below. +---------------+ | F1 INPUT | | F2 QUERY | | | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | | | +---------------+'0*((@@ ` ` INPUT MATERIAL PROPERTIESThe F1 INPUT key produces prompts for material set definition. Thefirst prompt on the data entry line requests the integer materialset number to be defined. ENTER MATERIAL SET NUMBER #Up to 10 material property sets may be defined and should bedefined in numerical order. Material property sets may includesome physical properties depending on the element type. Eachelement in the model has a material set number associated with itwhich defines its material properties. If different material orphysical properties exist in different parts of the structure thenmultiple material sets should be defined before elements aredefined so that the correct assignments may be made at the time ofelement definition.The next prompt requests the property values which are dependent onthe element type that has been selected. The prompts are: for truss elements, ENTER E, A FOR MATERIAL # M for beam elements, ENTER E, A, I, C FOR MATERIAL # M for 2-D plane and axisymmetric elements, ENTER E, NU FOR MATERIAL # Mwhere,E is the modulus of elasticity, A is the member cross section area, I is the member area moment of inertia, C is the beam section distance from neutral axis to surface for bending stress computation, NU is the poisson's ratio, and M is the material set number.Any material set may be changed or corrected by reusing the F1INPUT key and entering the material set number and new data. ` ` QUERY MATERIAL PROPERTIESThis selection prompts for the material set number and follows witha list of the current data values for that material. ` ` NODE DEFINITION'0*((@@This selection branches to a menu to perform node operations. Nodes for truss and beam element models will all be defined in thissection. If the 2D automesh option is used for the 2D plane andaxisymmetric models then that should be done first and anyadditional node operations will be done in this section. The menuis +---------------+ | F1 DEFINE | | F2 GEN ROW | | F3 MOVE | | | | F5 DELETE | | F6 QUERY | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` DEFINE NODEA node is defined by its number and coordinate position. A promptwill appear on the data entry line to ENTER NODE #,X,Y,Z =To input a node, simply enter the node number, and its X, Y and Zcoordinates. The Z coordinate input is only required for 3D Trussmodels. The data must be separated by commas or spaces. Allleading blanks are ignored, but do not enter any trailing blanks. If the node is generated properly, it will be displayed on thegraphics screen if it lies inside the current window. The startingwindow is 10 units by 10 units, but it will change automatically ifany of the view options are exercised. Autoscale will resize thewindow so that all currently defined nodes fit inside. The promptrecycles so that the next node may be input. Terminate input bytapping the return or enter key.Nodes do not have to be defined in any specific order. Thenumbering plan should be made to maximize utilization of rowgeneration if 2D automesh is not used. The highest node numberdefined will appear as the number of nodes in the model summarydisplayed in the upper right corner box. Any nodes which areundefined and unused in element definitions when the model isfinished will be listed in the model input file to FEPC, but they'0*((@@will have fixed displacements so that they do not cause the modelsolution to fail.If a node number is entered which is already defined, a programmessage appears that the node is already defined and then requeststhe user's consent to change to a new definition. This preventsaccidental redefinition, but also allows for correction of nodecoordinates. ` ` GENERATE ROW OF NODESIf a row or line of equally spaced nodes need to be defined, theymay be program generated by defining the end nodes and then usingthis F2 GEN ROW selection. The first prompt is DETECT START NODEThe lowest numbered node of the row is found by positioning thecursor at the node and detecting it. Pressing the right mousebutton or return key(if no mouse is present) in response to eitherof the detect prompts will abort the generation. The second promptis DETECT END NODEFollowing the end node detection the prompt is to ENTER NODE NUMBER INCR [1] #The node increment is the integer value added to the start nodenumber to define the first generated node number, and then it isadded again for the next generated node, etc. The number intervalbetween the start node and end node must be evenly divisible by thenode number increment. The default value is 1 if the return key ispressed without entering a numerical value. ` ` MOVE NODEThis selection allows any node to be moved by repositioning on thegraphics screen. This is useful if an element is badly shaped andmoving a node will improve its shape. It should be used primarilyfor nodes internal to the structure boundary because it is not asaccurate as input of numerical values for the boundary points. Thefirst prompt is DETECT NODE'0*((@@After detecting the node the prompt is DETECT NEW POSITIONMove the cursor to the new location of the node and detect it. ` ` DELETE NODEThis key produces a prompt to detect the node to be deleted. Following detection the node is deleted, and all elements whichuse this node in their definition will also be deleted. When anelement is deleted all higher numbered elements have their numberreduced by 1. ` ` QUERY NODEThis key produces a prompt to detect the node and then its numberand coordinates are displayed. ` ` ELEMENT DEFINITIONThis selection branches to a menu to perform element operations. Elements for truss and beam element models will all be defined inthis section. If the 2D automesh option is used for the 2D planeand axisymmetric models then that should be done first and anyadditional element operations will be done in this section. Themenu is +---------------+ | F1 SELEC MATL| | F2 DEFINE | | F3 GEN ROW | | F4 MODIFY | | F5 DELETE | | F6 QUERY | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+'0*((@@ ` ` SELECT MATERIAL SETThis function selects the material set assignment for elements tobe defined after this selection and is identified as the currentmaterial in the model summary window. The initial material setassignment for all elements is 1. This value is assigned to allelements as they are created. If a different assignment is neededfor some elements then the current material must be changed priorto defining the elements. The prompt is ENTER MATERIAL SET NUMBER #Enter the integer set number to be assigned to the next elementscreated. If more than one material is to be assigned the materialset properties must already be defined for the program to allowchange of the current material. ` ` DEFINE ELEMENTThis selection defines single elements by user selection of nodesfor each element. The user is prompted to detect each node neededfor the element definition. The order of node selection on twonode elements is of no consequence.THE NODES FOR FOUR NODE ELEMENTS MUST BE DEFINED IN ACOUNTERCLOCKWISE ORDER SURROUNDING THE ELEMENT AREA.Elements are numbered in numerical order as they are defined. Their material set assigned is the current material set. Eachelement is drawn on the graphics screen as it is defined. The nodeprompts recycle to define the next element and will continue untilthe right mouse button is pressed or the return or enter key ispressed at the node detect prompt to terminate element definition. ` ` GENERATE ROW OF ELEMENTSIf a row or sequence of elements can be defined by adding a singleinteger value to the node numbers of one element to define the nextelement then this function will do the generation. The firstprompt is DETECT LEAD ELEMENT'0*((@@Position the cursor at the center of the element which has the nodepattern to be incremented to generate the next elements and detectit. The next prompt is NO. OF ELEMS TO GENERATE #Enter the number of elements to be generated from the lead element. The last prompt is NODE NO. INCR TO GEN ELEMS [1]#Enter the integer value to be added to the lead element nodenumbers to define the first generated element and successively allthe elements to be generated. The return key will give a defaultnode increment value of 1. ` ` MODIFY ELEMENTAfter an element has been defined it may be modified by change ofmaterial or change of node definition. The submenu is +---------------+ | F1 CHG MATL | | F2 CHG NODES | | | | | | | | | | | | F10 PREV MENU| | | | | | PICK A | | FUNCTION | +---------------+Function key F1 produces a prompt to ENTER MATL #Enter the new material set number for the elements to be selected. The properties for the set must have already been input. The nextprompt is to detect the element. Position the cursor at theelement center and detect it. The prompt cycles for additionalelements to change to the new material until the right mouse buttonis pressed or a return key entry terminates input.Function key F2 produces a prompt to detect the element and'0*((@@following element detection, prompts appear to detect the new nodesdefining the element. ` ` DELETE ELEMENTThis function prompts to detect the element and following detectiondeletes it. When an element is deleted all higher numberedelements have their label(number) reduced by 1. The promptrecycles until the right mouse button is pressed or a return keyentry terminates deletions. ` ` QUERY ELEMENTThis function prompts to detect the element and following detectionlists the element number, its node numbers and material set number. Pressing the right mouse button or a return key entry terminatesqueries. ` ` RESTRAINTSThis section is for applying node displacement boundary conditions. By default all nodes displacement components are free to take onnonzero values appropriate to the structure response under load. The components which must be zero for the model to behave properlyare specified to be fixed. The following menu is displayed. +---------------+ | F1 SET VALUES| | | | | | | | F5 DELETE | | | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+'0*((@@ ` ` SET VALUESThis function sets the restraint condition to be applied to thenodes which are to be detected. A prompt appears to SET X-TRANSLATION BOUNDARY CONDITIONfollowed by the submenu +---------------+ | F1 FREE | | F2 FIXED | | F3 ANGLE | | | | | | | | PICK A | | FUNCTION | +---------------+Selection of F1 or F2 sets the x displacement component. Selectionof F3 will prompt to ENTER INCLINED BOUNDARY ANGLE (-89.99 TO +89.99 DEG. FROM X) =Enter an angle in decimal degrees from the x-axis in the range of-89.99 to +89.99 degrees. This will slave the x and ydisplacement components together such that the node can only movealong the line making this angle with the x-axis. Neither the xnor y displacement will be fixed to zero, but it constrains nodemotion to a line which is not parallel to the x or y axis. Afterthe angle is specified the program prompts to detect nodes whichare to have this restraint.If the x displacement component is free or fixed the next prompt is SET Y-TRANSLATION BOUNDARY CONDITIONfollowed by the submenu +---------------+ | F1 FREE | | F2 FIXED | | | | | | | | PICK A | | FUNCTION | +---------------+'0*((@@Select the y displacement condition.If the element type is a beam then the next prompt is SET Z-ROTATION BOUNDARY CONDITIONor, if the element type is a 3D truss the next prompt is SET Z-TRANSLATION BOUNDARY CONDITIONfollowed by the submenu +---------------+ | | | F1 FREE | | F2 FIXED | | | | | | | | | | | | PICK A | | FUNCTION | | | +---------------+The z-rotation boundary condition for beam elements is the noderotation component whose vector points in the z direction for beamelements lying in the x-y plane.After setting the restraint values, the prompt appears to detect anode. Following detection the restraint is plotted graphically bytriangles pointing in the direction of translation restraint at thenode. The graphic representation of the rotation restraint forbeams is a leftward descending line from the node with an arc atits end. Continue to detect all nodes to which this restraintcondition is to be applied. Terminate by pressing the right mousebutton or a return key entry, and reset the restraint conditionsfor other nodes. ` ` DELETE RESTRAINTThe restraint condition on any node may be removed by this functionfollowing the node detection. ` ` LOADS'0*((@@This section is for applying loads to the model. The menu for loadapplication is +---------------+ | F1 NODE FORCE| | F2 PRESSURE | | | | F4 DELET FORC| | F5 DELET PRES| | F6 QUERY FORC| | F7 QUERY PRES| | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` NODE FORCEThis function accepts node force component input and applies it todetected nodes. The first prompt is ENTER X FORCE =Input the value of the x-component of force. The next prompt is ENTER Y FORCE =Input the value of the y-component of force. If the element typeisthe beam the next prompt is ENTER Z MOMENT =or, if the element type is a 3D truss the next prompt is ENTER Z FORCE =At the detect node prompt detect all the nodes which carry theseforce components. When each node is detected graphic symbols ofthe loads are plotted at the node. The forces are represented withan arrow scaled relative to the maximum value of load and pointingin the direction corresponding with the load's sign. If a higherload value is entered later these vectors will rescale to thehigher value. Moment loads on beam elements are represented by a'0*((@@rightward ascending line with a ccw curved hollow arrow at the end. It is not scaled nor sign dependent. Terminate detection byclicking the right mouse button or a return key entry(if no mouseis present). Select F1 again to change the load set and pickother nodes. ` ` PRESSUREThis selection calls for input of a uniform pressure load and thenapplies it to all detected element edges. Only models using the2-D solid plane stress, plane strain or axisymmetric elements areallowed to be pressure loaded. For a new model the first action isto determine all the surface element edges. A message willappear while the list of edges is being computed. Only surfaceedges may have an applied pressure load. The pressure load isconverted to node forces by the program so only the resultant nodeforces will be printed in the *.LST file. A negative value may beentered for a 'tensile' pressure. The prompt is ENTER ELEMENT EDGE PRESSURE =Input the value of the pressure. The next prompt is to detect theelement edge. At each detection two lines parallel to the edgewill be drawn symbolizing the pressure load. Continue detectinguntil all edges with the given pressure load are detected. Selectthe F2 PRESSURE key again to enter a new value of pressure to beapplied to other element edges in the model. ` ` DELETE FORCThis selection calls the detect node prompt to delete the forcesapplied to detected nodes. ` ` DELETE PRESThis selection calls the detect edge prompt to delete the pressureapplied to detected edges. ` ` QUERY FORC'0*((@@This selection calls the detect node prompt to list the values ofapplied loads at the detected node. ` ` QUERY PRESThis selection calls the detect edge prompt to list the values ofpressure at the detected edge.2.3 2D AUTOMESH GENERATIONThis section of the program is used for area mesh generation oftwo-dimensional plane stress, plane strain, or axisymmetric models. The principle of the approach is a mapping of an integer area gridinto the geometrical area of the model. The geometrical area isdefined using point locations, lines, and arcs. The perimeter ofthe geometrical area is defined by the complete set of lines andarcs which enclose the area.The integer area grid will have lines which correspond to the linesand arcs of the geometrical area. Plan the correspondence byimagining or physically sketching on square grid paper theperimeter in the integer area. Use integer coordinates I and Jwith a range of 1 to IMAX and 1 to JMAX respectively. IMAX andJMAX values are listed in the first section of this guide. A 1 by1 square in the integer area grid will map to an element in thegeometrical area. Grid points in the integer area grid will map tonode points in the geometrical area model.Lines in the integer area can only be lines of constant I or Linesof constant J. The perimeter must be defined by a head-to-tailconnection of lines in a counterclockwise(ccw) direction around thearea. The length of line in the integer area is equal to thenumber of elements desired along the corresponding line or arc inthe geometrical area.The process involves defining the geometrical points needed todescribe the model area, then defining lines or arcs using thosepoints which complete the model perimeter. Next plan thecorresponding integer area grid to be mapped into the geometry ofthe model.After all the geometric points, lines, and arcs have been entered,area mesh generation can begin. By default, the element edgelengths along any line or arc are uniform in size. In order tobias the relative element sizes to refine the mesh in local areasan element size feature is implemented. The relative element size'0*((@@at any defined point may be specified before generating the mesh. See the menu explanation below.The genmesh function presents a prompt to pick the starting pointof the area. This point on the geometry will correspond to the 1,1I,J coordinate location on the integer area. A series of promptsthen proceed for the detection of a line or arc, the number ofelements on that line or arc, and the direction of thecorresponding line in the integer I,J area.The first line or arc detected must have the selected startingpoint as one of its end points. The next line or arc picked musthave the other end point of the first line or arc as one of itsend points. Each successive line or arc picked must then connectto the other end point of the previous line or arc. Thiscontinues until the perimeter of the geometry is closed and the endpoint of the last line in the integer area must be back at thestarting point, i.e., the perimeter in the geometry area and theperimeter in the integer area must close simultaneously. Both ofthese perimeters must progress ccw around the area. A graphicdisplay of the integer area lines is shown in the lower right sidebox as each line is selected and specified. This shows theprogress around the perimeter and when the perimeter closes.When a line or arc is picked the entry of number of elementsdetermines the length of the line in the integer area. Thedirection entry chooses one of four allowable line directions inthe integer area. The directions are labeled 1, 2, 3, and 4, whichcorrespond to right(+I), up(+J), left(-I), and down(-J)respectively in the I,J coordinates.The integer area of the model must lie in the positive quadrant ofI,J coordinates. Since the starting point in the integer area isat 1,1, and the perimeter must be ccw, the direction for the firstline or arc must be 1. The direction for the second line or arcpicked may be 1 or 2. Successive lines may have any directionvalues as long as some lines with directions 1 and 2 are usedbefore any with directions 3 or 4 so that the I and J coordinatevalues always remain positive. The total number of elements on alllines in the 1 direction must match the total number in the 3direction, and the total number in the 2 direction must match thenumber in the 4 direction.The bandwidth of the structure stiffness matrix is minimized bymaking the number of elements in the I direction smaller than inthe J direction. The limits are IMAX-1 elements in the I directionand JMAX-1 elements in the J direction. However, no model may havemore than the maximum number of nodes or elements listed in thefirst section of this guide.Mapping is an iterative process of distorting the integer area tofit in the geometry area. After a few iterations a mesh will be'0*((@@drawn on the screen. If it appears to be suitable then it can beaccepted or more iterations may be requested to make it smoother. If it is unacceptable then a different integer area may be tried.The menu of functions for mesh generation is +---------------+ | F1 POINT | | F2 LINE | | F3 ARC | | F4 ELEM SIZE | | F5 GENMESH | | | | | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` POINTPoints are used to define lines and arcs which make up the model'sgeometric perimeter. Two points are needed to define a line, andthree points along the arc are needed to define an arc. Pointsare input by their coordinate location. Selection of key F1produces a submenu. +---------------+ | F1 CREATE | | F2 MODIFY | | F3 DELETE | | | | | | F6 QUERY | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+'0*((@@ ` ` CREATE POINTA point is created in response to the prompt ENTER X,Y FOR POINT #NThe nth point is plotted on the graphics screen using the + symbolfollowing the x,y coordinate entry. The prompt recycles foradditional point entries until a return key entry terminates pointinput. Additional points may be entered later by accessing thepoint function again. ` ` MODIFY POINTThis function allows a defined point to be moved to anotherlocation. A detect point prompt picks the point to move, and theprompt for coordinate input appears. Modifying pointsautomatically modifies any existing lines or arcs using themodified point. ` ` DELETE POINTA detect point prompt picks the point to delete, and followingdetection it is deleted. The space in the program array is notrecovered, however, so it is preferable to use the modify functionto move any unused points to a location where they are usable. Deleting points automatically deletes any existing lines or arcsusing the deleted point. ` ` LINEA straight line may be used to represent all or part of anystraight edge on the model. More than one line on an edge might beused to produce different element spacings along the edge. If twoor more lines are used on any single edge, they should beconnected in series with no overlap. Selection of key F2 producesa submenu.'0*((@@ +---------------+ | F1 CREATE | | F2 MODIFY | | F3 DELETE | | | | | | F6 QUERY | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` CREATE LINEA line is defined by picking two points at the ends of the line. The first prompt is DETECT POINT 1Position the cursor at the point and detect it. The next prompt is DETECT POINT 2Following detection of the second point the line is drawn. Theprompts recycle until terminated by clicking the right mousebutton or pressing the return key(if no mouse is present) at thedetect point 1 prompt. ` ` MODIFY LINEIf a line was defined incorrectly or no longer useful it may bemodified by this function. The first prompt is to detect the line. Position the cursor at the center of the line to detect it. Following detection are the prompts to detect the two new points. ` ` DELETE LINEA line may be deleted by detecting the line at the prompt. However, the space in the program array is not recovered so it is'0*((@@preferable to modify it if another line is needed. ` ` ARCAn arc may be used to represent all or part of any circular arc onthe model of 180 degr. or less included angle. If more than onearc is used on a circular arc of the model then they should beconnected in series. Three points along the arc are needed forthe definition. They are the two end points and an intermediatepoint. Another point is created during definition of the arc atthe arc's center of curvature. This may cause the autoscalefunction to reduce the model scale substantially if the arc radiusis very large in order to fit all the points on the graphicsscreen. Selection of key F3 produces a submenu. +---------------+ | F1 CREATE | | F2 MODIFY | | F3 DELETE | | | | | | F6 QUERY | | | | F8 VIEW OPTS | | F9 DSPLY OPTS| | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` CREATE ARCAn arc is defined by picking three points sequentially along thearc. The first prompt is DETECT START POINT 1Position the cursor at the point and detect it. The next prompt is DETECT MID POINT 2Position the cursor at the point and detect it. The next prompt is DETECT END POINT 3'0*((@@Following detection of the third point the arc is drawn. Thprompts recycle until terminated by the right mouse button or areturn key entry at the detect start point 1 prompt. ` ` MODIFY ARCIf an arc was defined incorrectly or no longer useful it may bemodified by this function. The first prompt is to detect the arc. Position the cursor at the mid point of the arc and detect it. Then the prompts to detect the new three points will follow. ` ` DELETE ARCAn arc may be deleted by detecting the arc at the prompt. However,the space in the program array is not recovered so it is preferableto modify it if another arc is needed. ` ` ELEMENT SIZESelection of the ELEM SIZE function prompts to DETECT POINTAfter detection of a point the prompt follows to ENTER ELEMENT SIZE (RELATIVE TO 10.0) =Enter a value that will bias the mesh in the desired manner. Forexample, a value of 5.0 will make the element edge length nearestthe point half the size of the other end if its point has a valueof 10.0. ` ` GENERATE MESHSelection of the GENMESH function begins a series of prompts andinputs to define the meshing area. If the element type has notbeen selected the element menu will be presented for a choice. Ifmore than one material set has been defined then the prompt to ENTER MATERIAL SET NUMBER #'0*((@@will appear. Enter the set number which will be as to allthe elements defined using the mesh generator.Following these conditional entries the prompt is to DETECT START POINTThis is a geometric point on the model which corresponds to the 1,1point in the I,J integer area. Next the prompt to DETECT LINE OR ARCbegins the sequence of perimeter definition. Detect the line orarc which connects to the starting point and starts on the ccw patharound the perimeter. Following detection ENTER NUMBER OF ELEMENTS #along the line or arc. Then ENTER DIRECTION #of the line in the integer area(1, 2, 3, or 4). The integer arealine then appears in the lower right side box. The set of promptsto detect line or arc, enter number of elements, and enterdirection all cycle until the user terminates input by clicking theright mouse button or pressing the enter key(if no mouse ispresent). The user should be sure the geometry perimeter is closedby checking the right side graphic of the integer area beforeterminating. The program checks that the integer area is closed,and if so begins iterating on the mapping. This may take a fewminutes.If the integer area is not closed a program message reports thiscondition and the geometry is redrawn. Another trial to input theperimeter may begin with selection of the automesh function.If the integer area did close, after a few iterations the mesh isdrawn on the screen with the prompt MORE MESH ITERATION (Y OR N)?If it needs additional smoothing answer Y. More iterations will bedone and the prompt will reappear. If it looks acceptable or it isto be redone differently then answer N.The next question is OK TO KEEP (Y OR N)?Enter Y to keep the mesh, or enter N to discard this mesh and redothe GENMESH function with another plan.'0*((@@Once an acceptable mesh of nodes and elem kept, return tothe model data menu to apply the displacement boundary conditionsand loads, and perhaps define a material property set.When the model data is complete go to the files menu and store themodel and analysis files to disk. This should also be doneperiodically during building of the model in case of unexpectedtermination of the session or a different path is chosen tocomplete the model.2.4 VIEW OPTIONSThis selection appears on many of the branch menus to allowexercising the view options without retracing the menus to reachthem. The following menu appears on selection of view opts. +---------------+ | F1 AUTOSCALE | | F2 ZOOM | | F3 MAGNIFY | | F4 CENTER | | F5 3D VIEW PT| | F6 2D XY VIEW| | | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` AUTOSCALESelection of autoscale automatically scales the graphics window toinclude all currently defined points and nodes. ` ` ZOOMThis function allows the user to select a portion of the graphicswindow which is then scaled to fit the full window. The firstprompt is'0*((@@ SELECT NEW WINDOW CORNERPosition the cursor at one corner of the zoom area and detect it. The next prompt is SELECT OPPOSITE CORNERPosition the cursor at the opposite corner of the zoom area anddetect it. ` ` MAGNIFYThis option changes the size of the model displayed. The prompt is ENTER THE MAGNIFICATION FACTOR =A positive value must be entered; values larger than one willincrease the size of the drawing and values smaller than one willdecrease the size.Subsequent use of the magnify command will enlarge (or decrease)the model display with respect to its current size. For example,magnifying the model by two and then by three produces an image sixtimes larger than the original. ` ` CENTERThe model may be moved by selecting a new center of the graphicswindow. The prompt is LOCATE NEW CENTER, PRESS SPACE BARPosition the cursor where the graphics window center is to be anddetect it. ` ` 3D VIEW POINTSelection of this function prompts to ENTER LOCATION OF EYE VIEWPOINT _ X,Y,Z =After entering the values, the graphic display is redrawn with aview from the eye viewpoint.'0*((@@ ` ` 2D XY VIEWThis function resets the view to the x,y plane and autoscales it.2.5 DISPLAY OPTIONSDisplay options control which entities and labels are visible whena graphics plot is done. A branch menu appears. +---------------+ | F1 ENTITY SW | | F2 LABEL SW | | | | F4 MONO/COLOR| | | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+ ` ` ENTITY SWITCHAn entity switch setting is off or on to control the individualentity's visibility. Selection of this function brings up asubmenu. +---------------+ | F1 POINTS | | F2 LINES | | F3 ARCS | | F4 NODES | | F5 ELEMENTS | | F6 RESTRAINTS| | F7 LOADS | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+' 0*((@@Selection of a function key will produce a prompt to change current setting by default. If the visibility is 'on' the promptis OK TO SWITCH OFF [Y]#A Y or return key entry will switch the visibility 'off'. ` ` LABEL SWITCHThis function controls the display of labels(numerals) on thegraphic model. The submenu is +---------------+ | F1 NODE NOS | | F2 ELEMNT NOS| | | | | | | | | | F10 PREV MENU| | | | PICK A | | FUNCTION | +---------------+Selection of a function key will produce a prompt to change itscurrent setting by default. If the display is 'off' the prompt is OK TO SWITCH ON [Y]#A Y or return key entry will switch the display 'on'. ` ` MONO/COLORThis function switches the display between black and white or colorwhen the computer has a VGA graphics board. On other graphicsboards the display is always black and white. Switching the VGA toblack and white allows the screen graphics to be dumped to a blackand white printer without loss of character intensity as sometimeshappens when screen dumping color graphics to a black and whiteprinter. Since only the drawing color palette is changed with thisswitch the change occurs when the next drawing is done after theswitch. Execute the function key again to return to a colordisplay.'!0*((@@ 3.0 THE ANALYSIS BY FEPCWhen a model has been developed and saved, it is complete and readyto be processed by the finite element processor, FEPC. After exitfrom FEPCIP, and before starting FEPC, be sure that thefilename.ANA file can be accessed by FEPC by copying it to theFEPC diskette in the same directory where FEPC.EXE resides, or byusing the drive and path designation in the filename.3.1 RUNNING FEPCWith the FEPC.EXE file in the current drive and directory, begin bytyping FEPCAfter the FEPC logo appears, a prompt will appear to enter themodel filename (with drive and/or path designation but without the.ANA extension),(20 characters max).As the computations proceed, messages will appear on the screenreporting the computation step in progress. If errors occur, errormessages will also appear on the screen. FEPC creates some otherfiles as it runs. There is a listing file of all the printedoutput labeled filename.LST. This file should be studied by theuser after an analysis to check the input data interpreted by FEPCand all the numerical output. A file labeled filename.MSH storesthe node and element data for FEPCOP. A file labeled filename.NVLstores the node displacement and element stress data for FEPCOP.Some other files are also created during the FEPC run which aredeleted upon normal termination of the program so the disk whichstores the .ANA file should have some excess space for these filesduring runtime. If the run terminates abnormally some of thesefiles may still be on the disk with extensions of .ELM and .LOD. These and other output files will be overwritten when running amodel with the same filename.If the FEPC run was successful then FEPCOP may be used to displaythe results in graphic form. If the run was not successful thenexamine the filename.LST file for data errors or error messages'"0*((@@that may help to correct the model.3.2 THE FEPC OUTPUT, FILENAME.LST, FILEThe output from a FEPC run is stored in a listing file calledfilename.LST, where the filename is the same as the model file nameentered when beginning the FEPC analysis. This file includes alisting of all the input data as well as all the numerical results.It begins with the job title followed by a summary of some of thecontrol data. The number of node points in the model is givenalong with the number of element groups and load cases. Allmodels prepared by FEPCIP will have only one element group and oneload case although the FEPC program allows more. The location anddisplacement boundary conditions for all nodes are listed next. The z displacement boundary condition should be fixed for all 2Dtruss and 2-D solid models. For beam element models it correspondsto the node rotation component and may be fixed or free. Then agroup headed EQUATION NUMBERS follows. Each degree-of-freedom inthe model has an associated equation in the set of simultaneousequations to solve for the displacement components of every node. Every displacement component which is fixed by a boundary conditionis then eliminated from the set of equations. This equation numberlist is useful if the program fails to execute and reports errormessage 10 described in the next section.The load case data list all the node point loads by node number,direction, and magnitude. These should agree with the input donein FEPCIP. However, if a pressure load was input in FEPCIP thenthe node forces are those calculated to give the correct pressureapplication to the model. Next the element data begins with thedefinition of material property sets. The property values for eachset are listed. Then the element definition of all elementsfollows. The elements are defined by the list of node numberswhich form the geometry of the element and the material propertyset which matches the material forming the element. This concludesthe input data listing of the model.The output data begins with a summary of the system equations. Thenumber of equations, the number of terms inside the profile of thestructure stiffness matrix, the maximum bandwidth, and the averagebandwidth are reported. This gives a feeling for the size of theproblem and the effectiveness of the node numbering pattern inminimizing the bandwidth.The displacement values for all node components are listed. Displacements for all fixed node components should be zero. The zdisplacement components will generally be zero, except for the beam'#0*((@@element models in which they are the rotation components.Stress output is related to the element type used in the analysis.In truss element models the axial force and stress are reported. In beam element models the axial, flexure and average shear stressare reported, followed by a similar report of the axial force, thebending moments and lateral force. The sign conventions are thatthe force and moment vectors are positive when pointing in positivecoordinate directions. A local coordinate system for each elementmay be set up using the first node I as the origin and pointing theaxial coordinate toward the second node J. If that coordinatepoints to the viewer's right then the lateral coordinate is upwardand the third coordinate points toward the viewer.In this local coordinate system a positive axial force at node Iresults in a compressive axial stress which is constant along theelement length. A positive moment at node I results in a tensilestress on the top surface which is the value printed in the file. The moment varies linearly from node I to node J. A positivemoment at node J results in a compressive stress on the top surfaceof the beam element. This is consistent with simple beam theory inwhich a positive moment vector on the right end and an equalnegative moment vector on the left end produce a compressive stresson the top surface. A positive shear force at node I balances anequal negative shear force at node J, and this is usually definedas a positive shear stress in simple beam theory conventions.Stress components for 2-D plane stress or plane strain analysesthat are listed are the two normal stresses and the shear stressin the x,y plane. Also, the Von-Mises equivalent or effectivestress is calculated. For axisymmetric solid models the sameinplane components are given along with the hoop stress component. The x component is in the radial direction, the y component isparallel to the axis of symmetry and the t component is the hoopvalue. The Von-Mises equivalent stress is also calculated in thiscase.3.3 FEPC ERROR MESSAGES1 - OUT OF SPACE, MODEL IS TOO LARGE (I)X The model is too large to run in FEPC. Reduce the model sizein FEPCIP and try again. Consult the program limits given insection 1.(# 2 - NODE 'n' HAS BEEN PLACED ON AN INCLINED BOUNDARY, BUT IT IS ALREADY CONSTRAINED AGAINST X OR Y DISP. OR BOTHX An inclined boundary angle is specified for node n, but an xor y restraint was also specified which is incompatible. Editthe model in FEPCIP.(# '$0*((@@3 - FEPC.EXE FILE NOT FOUNDX The FEPC.EXE file must reside in the current drive anddirectory to execute.(# 6 - 'm' ELEM IS HIGHER THAN NO. OF ELEMENTS IN THE GROUPX The filename.ANA file has been corrupted because elementnumber m is higher than the total number of elements. The*.ANA file is an ASCII file so it may be printed or edited. Examine its contents in comparison with the data printout inthe filename.LST file.(# 7 - ELEMENT NO 1 IS NOT DEFINED FIRSTX The filename.ANA file has been corrupted because elementnumber 1 is not defined first in the list of elementdefinitions. The *.ANA file is an ASCII file so it may beprinted or edited. Examine its contents in comparison withthe data printout in the filename.LST file.(# 8 - YOU HAVE A ZERO LENGTH ELEMENT #'m'X A beam or truss element is defined using the same node forboth ends or the two nodes defining the element havecoincident coordinate locations.(# 9 - BAD ELEMENT #'m'X A quadrilateral element is improperly defined or is toodistorted. Check for cw node order definition around theelement (it should be ccw), inside angles between sidesgreater than 180 degrees, butterfly shaped element, or atriangle formed by using one node for two corners (this islegal if the last two nodes in the element definition are thesame).(# 10 - STIFFNESS MATRIX NOT POSITIVE DEFINITE, NEGATIVE STIFFNESS DIAGONAL TERM FOR EQUATION 'n', VALUE = '#'X During solution of the system equations a negative diagonalterm is found which means that the equations cannot be solved. The equation number corresponds to the free nodedegree-of-freedom in the system ordered consecutively withnode numbers. These are listed in the filename.LST fileproduced in the FEPC run. Find the node number from this listthen examine the elements which are defined using this nodenumber for errors. If the equation number is 1 or the lastequation number then the error is probably due to lack ofsufficient displacement restraints to prevent rigid bodymotion.(# 11 - INCLINED BOUNDARY ANGLE MUST BE BETWEEN -89.99 AND +89.99 DEGRX The inclined boundary angle input is outside the allowablerange.(# H&%0*((@@ 4.0 GRAPHIC RESULTS USING FEPCOPAfter a successful run by FEPC, results files, filename.MSH andfilename.NVL, will have been created on the disk. These are theinput files for output processing by FEPCOP.With the FEPCOP.EXE file in the current drive and directory, beginby typing FEPCOPwhere means press the enter or return key. After the FEPCOPlogo appears the program continues after a short pause.The screen will clear and a prompt will appear to ENTER MODEL FILE NAME (NO EXT) -Enter the filename (with drive and/or path designation but withoutthe .MSH or .NVL extension),(20 characters max). Some messageswill appear noting the progress of calculations, and then thescreen will clear and the FEPCOP MAIN MENU is displayed along witha prompt to PICK A FUNCTION. OUTPUT PROCESSOR FINITE ELEMENT PERSONAL COMPUTER DATE TIME TITLE: +---------------++--------------------------++-----------------+ | F1 DEFORMED || || | | F2 X-STRESS || || | | F3 Y-STRESS || || | | F4 XY-STRESS || || | | F5 T-STRESS || || | | F6 VON MISES || || | | F7 TRUSS STRS|| || | | F8 BEAM STRS || || | | F9 OPTIONS || || | | F10 EXIT || || | | || || | | || || | | PICK A || || | | FUNCTION || || | | || || | +---------------++--------------------------++-----------------+'&0*((@@4.1 DEFORMEDSelection of F1 DEFORMED brings up a branch menu. +---------------+ | F1 PLOT | | F2 ANIMATE | | | | | | | | | | | | F10 PREV MENU| | | | | | PICK A | | FUNCTION | +---------------+Selection of F1 PLOT produces a deformed shape plot of the elementmesh superimposed over the undeformed model. This plot shows thefinite element mesh when the node displacements are scaled andadded to the node coordinates so that the deformed shape isexaggerated. In truss and beam models the deformed mesh issuperimposed over the undeformed mesh plot. In 2-D solid modelsthe deformed mesh is superimposed over the outer boundary of theundeformed shape. The displacement scale factor may be changed inthe OPTIONS menu to increase or decrease the plotted deformation. An additional submenu appears for modifying the view of the plot. +---------------+ | F1 AUTOSCALE | | F2 ZOOM | | F3 MAGNIFY | | F4 CENTER | | F5 3D VIEW PT| | F6 2D XY VIEW| | F7 QUERY NODE| | | | | | F10 PREV MENU| | | | | | PICK A | | FUNCTION | +---------------+''0*((@@Functions 16 are the same as in FEPCIP. Function 7 prompts toDETECT NODE, then lists the displacement components of that node inthe upper right box. Clicking the right mouse button or pressingthe enter key (if no mouse is present) terminates the query mode.Selection of F2 ANIMATE produces a sequential mesh plot of trussand beam models or a boundary outline plot of 2-D models showingthe progressive deformation as the load is cyclicly applied. Pressany key to terminate the animation.The next five function key selections show the stress contour plotsdeveloped in 2-D solid models for the indicated components ofstress.4.2 X-STRESSThis function draws a contour plot of the X direction normalstress. It is accompanied by a legend of the contour values andthe view modification and query menu. Selection of the queryfunction lists the average nodal stress component value for thedetected node.4.3 Y-STRESSThis function draws a contour plot of the Y direction normalstress.4.4 XY-STRESSThis function draws a contour plot of the XY shear stress.4.5 T-STRESSThis function draws a contour plot of the T direction normalstress. This stress component is nonzero only for the axisymmetricelement models and represents the hoop stress in the axisymmetricstructure.'(0*((@@4.6 VON MISESThis function draws a contour plot of the Von Mises equivalentstress. This stress is calculated based on the distortion energyfailure theorem using all the stress components calculated in theloaded model.4.7 TRUSS STRSThis function is used to display the results in truss elementmodels. The user may select a plot of the axial force or stress inall truss elements. The plot is in a bar chart format with theheights scaled to the maximum value in any element. Plus or minussigns are drawn on the bar near the top to indicate whether themember is in tension or compression.4.8 BEAM STRSThis function is used to display the results in beam elementmodels. The user may select to plot the axial, flexure, averagetransverse shear, or the maximum combined axial plus flexurestress. These are also in bar chart format with signs indicatednear the top of each bar. The axial and transverse shear stressesare constant along an element length so one bar per element issufficient. The flexure stress component varies linearly along theelement length so a bar is plotted for the value at each end. Twobars are also plotted for the combined axial plus flexure stress. The sign of the combined stress is the same as the sign of theaxial stress which is the combination producing the largestmagnitude.4.9 OPTIONSFunction key F9 OPTIONS produces a submenu. +---------------+ | F1 NODE SW | | F2 ELEM SW | | F3 DISP SCALE| | F4 MONO/COLOR| | F5 COLOR FILL|')0*((@@ | | | | | F10 PREV MENU| | | | | | PICK A | | FUNCTION | +---------------+Selecting F1 adds node symbols to the 2-D stress plots, and F2 addselement outlines inside the 2-D boundary for stress plots. Both ofthese selections produce a prompt to switch the current setting tooff or on. Answering Y or by default a return key entry will makethe change. Selection F3 allows the scale factor for the deformedshape plots to be changed by prompting for a new scale factor withthe current scale factor shown as the default value. Enter alarger value to increase the exaggeration or a smaller value todecrease it. The MONO/COLOR function is the same as in FEPCIP. The COLOR FILL function switches the colored line contour plot toa color filled plot or vice versa.4.10 EXITSelecting F10 exits the FEPCOP program.*0*((@@ 5.0 SETUP OF THE PROGRAMSThe programs executable files, a README file, this user's guidefile and some sample model and analysis files are supplied on one3.5 in. diskette. First, make backup copies of all the files. Then copy the *.EXE files to any drive and directory you wish tooperate them from. The data files may be in another directory. Files that are created during execution of FEPC will reside in thesame directory with the *.ANA file. The programs will also workwhen copied over to a hard disk drive. There are also some samplemodel, *.MOD, and analysis, *.ANA, data files on the disks whichcan be recalled into FEPCIP or run in FEPC.