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1 C:\files\classes\fem\program code\truss\truss solve\truss.f ! truss.f90! Kurt Gramoll! 2 Feb 2018! Requires input file as part of the command string (assumes.dat)! Format! line 1: number of nodes, number of elements! line for each node! node#, constraint(0,1,2,3)(none,x,y,both), locx, locy, forcex, forcey! line for each element! element#, left node#, right node#, E, Area! Sample From Logan book, example 3 5! 4 3! ! ! ! ! e6 2.0! e6 2.0! e6 2.0!=======1=========2=========3=========4=========5=========6=========7=========8=========9=========10========11 program truss implicit none!! NOT USED, example of set dimension for array (old Fortran method)!! assuming maximum nodes=50, max elements=50!! real*8 :: gstiff(1:100, 1:101)! global stiffness matrix with RHS, size = numnodes*2, array start at 1!! real*8 :: gstiff(100, 101)! global stiffness matrix with RHS, size = numnodes*2, array start at 1 real*8, allocatable, dimension(:,:) :: gstiff, gstifforig!! dynamic array method real*8, DIMENSION(1:4,1:4) :: elemstiff!! one for each element, old syntax real*8, allocatable, dimension(:) :: nodelocx, nodelocy!! location of node real*8, allocatable, dimension(:) :: load, disp!! node force (RHS) and displacement real*8, allocatable, dimension(:) :: elemlen, stress, angrad!! element length, stress, orientation angle (in radians) real*8, allocatable, dimension(:) :: youngmod, area!! element modulus and area real*8 :: temp, temp1, sum!! real = real*4 (single), real*8 (double, 64 bits), real*16 (quad)

2 C:\files\classes\fem\program code\truss\truss solve\truss.f real*8 :: cosang, sinang!! cosine and sine of each element bar real*8 :: elapsedtime, t1, t2!! used for calculation time integer, allocatable, dimension(:) :: noderest!! type of restriction, 0=non, 1=disp x, 2=dips y, 3=both integer, allocatable, dimension(:) :: leftnode, rightnode!! node order, left to right integer :: i, j, k, n, m, irow, icol, ielem, inode!! counters integer :: numnode, numelem, dof!! node, element and total degree of freedom character (len=100) :: strbuffer100!! string that holds command line argument character (len=30) :: filename, fileinname, fileoutname! file name (no ext), file name in and out w/ ext!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Get command line input parameters, call for each item call GETARG(1, strbuffer100)! special function to read in argurments read (strbuffer100,*) filename! reading in file name (no extension) fileinname = TRIM(fileName) // ".txt"! file in name with extension fileoutname = TRIM(fileName) // "_out.txt"! file out name with extension!! write to console that program (1st *) has started, free format (2nd *) write (*,*) 'truss program start reading in data from: ', fileinname CALL CPU_TIME(t1)! set timer, used to determine total time program runs!! Read in data file ======================================================================== open (UNIT=5, FILE=fileInName)! file number 5 standard for input, could use 'open (5, fileinname)' read (5,*) numnode, numelem! Just one line, needed to figure DOF (used for matrix setup!! need to allocate memory for dynamic matrices, needed for load and disp vector size before reading dof = 2*numNode allocate (gstiff(dof, dof))!! used when reducing global stiffness matrix to solvable set of equations (b.c. applied) allocate (gstifforig(dof, dof)) allocate (load(dof))! external loads at each node, b.c. (maybe unknown) allocate (disp(dof))! unknown node displacements (some known, b.c.) allocate (nodelocx(numnode)) allocate (nodelocy(numnode)) allocate (noderest(numnode))! node restriction (i.e. B.C.), 0 = none, 1 = x, 2 = y, 3 = both allocate (leftnode(numelem))! node 1 in local numbering allocate (rightnode(numelem))! node 2 in local numbering

3 C:\files\classes\fem\program code\truss\truss solve\truss.f allocate (youngmod(numelem)) allocate (area(numelem)) allocate (angrad(numelem))! calculate from nodelocx and nodelocy allocate (elemlen(numelem))! calculate from nodelocx and nodelocy allocate (stress(numelem))! to be found leftnode ( : ) = 0 rightnode ( : ) = 0!! Finish reading in data now that matrices sizes are set read (5,*) (n, noderest(i), nodelocx(i), nodelocy(i), load(2*(i 1)+1), load(2*(i 1)+2), i=1, numnode) do i = 1, numelem!! long way to read in read (5,*) n, leftnode(i), rightnode(i), youngmod(i), area(i)!! Write out copy of inputted data ============================================================ open (UNIT=6, FILE=fileOutName)!! file number 6 standard for output to file 'Number of points: ', numnode, '; elements: ', numelem "Nodes" write (6,62) (i, noderest(i), nodelocx(i), nodelocy(i), load(2*(i 1)+1), load(2*(i 1)+2), i=1, numnode) 62 format (" Pt Fixed loc X loc Y Force X Force Y" / (2I5, 4E12.4)) "Elements" do i = 1, numelem elemlen(i) = sqrt( (nodelocx(rightnode(i)) nodelocx(leftnode(i)))**2 + & (nodelocy(rightnode(i)) nodelocy(leftnode(i)))**2 ) write (6,63) (i, leftnode(i), rightnode(i), youngmod(i), area(i), elemlen(i), i=1, numelem) 63 format (" elem i j Modulus Area Length" / (3I5, 3E12.4))! Initialize global stiffness matrix ================================================= gstiff ( :, : ) = 0.0! or you can loop on matrix (slower)! Construct element stiffness ====================================================== do ielem = 1, numelem! atan or datan (real*8) returns radians temp = nodelocy(rightnode(ielem)) nodelocy(leftnode(ielem)) temp1 = nodelocx(rightnode(ielem)) nodelocx(leftnode(ielem)) angrad(ielem) = datan( temp / temp1 )! put in array, use again for stress

4 C:\files\classes\fem\program code\truss\truss solve\truss.f cosang = cos(angrad(ielem)) sinang = sin(angrad(ielem)) temp = area(ielem) * youngmod(ielem) / elemlen(ielem) elemstiff(1,1) = temp*cosang**2 elemstiff(1,2) = temp*cosang*sinang elemstiff(1,3) = elemstiff(1,1) elemstiff(1,4) = elemstiff(1,2) elemstiff(2,1) = elemstiff(1,2) elemstiff(2,2) = temp*sinang**2 elemstiff(2,3) = elemstiff(2,1) elemstiff(2,4) = elemstiff(2,2) elemstiff(3,1) = elemstiff(1,1) elemstiff(3,2) = elemstiff(1,2) elemstiff(3,3) = elemstiff(1,3) elemstiff(3,4) = elemstiff(1,4) elemstiff(4,1) = elemstiff(2,1) elemstiff(4,2) = elemstiff(2,2) elemstiff(4,3) = elemstiff(2,3) elemstiff(4,4) = elemstiff(2,4)!write (*,71) ( (elemstiff(n, i), i=1, 4), n=1, 4) 71 format ((4F9.3))! put element stiffness into global matrix i = leftnode(ielem) j = rightnode(ielem) do n = 1, 4 do k = 1, 4!! do each pair differently if (n < 3) irow = 2*(i 1) + n if (n >= 3) irow = 2*(j 1) + n 2 if (k < 3) icol = 2*(i 1) + k if (k >= 3) icol = 2*(j 1) + k 2 gstiff(irow, icol) = gstiff(irow, icol) + elemstiff(n, k)

5 C:\files\classes\fem\program code\truss\truss solve\truss.f gstifforig = gstiff!! save orginal for later to get all forces at nodes!! testing output, small matix only!write (6, 65) ( (gstifforig(n, i), i=1, dof), n=1, dof) 65 format (/"Stiffness" / (8E9.2) )! Apply displacement boundary conditions ================================================! set fixed node direction to zero (row and column) except when i=j, then 1.0 do inode = 1, numnode! ZERO X deflection set row and column to zero except diagonal term to 1 if (noderest(inode) == 1.OR. noderest(inode) == 3) then! x dir fixed irow = 2*(iNode 1) + 1 do icol = 1, dof if (icol /= irow) then gstiff(irow, icol) = 0.0 gstiff(icol, irow) = 0.0 else gstiff(irow, icol) = 1.0! can be anything except 0 load(2*(inode 1)+1) = 0.0! load is also set to zero (when solving, gives defl = 0)! ZERO Y deflection set row and column to zero except diagonal term to 1 if (noderest(inode) == 2.OR. noderest(inode) == 3) then! y dir fixed irow = 2*(iNode 1) + 2 do icol = 1, dof if (icol /= irow) then gstiff(irow, icol) = 0.0 gstiff(icol, irow) = 0.0 else gstiff(irow, icol) = 1.0! can be anything except 0 load(2*(inode 1)+2) = 0.0!! Testing output!write (6, 65) ( (gstiff(n, i), i=1, dof), n=1, dof)

6 C:\files\classes\fem\program code\truss\truss solve\truss.f !write (6, 72) ( load(i), i=1, dof) 72 format (/"force" / (8F8.0))!================== Solve using Cholesky ======================================! Find all displacements, known displaces for zero still fine! Cholesky is a matrix factor method, decomposition is stored in lower triangle! RHS not effected, solution is stored in disp array!! MISSING SOLVER CODE! debugging console output!write (*, 74) ( disp(i), i=1, dof) 74 format (/"displacement" / (8F8.3))!! get all forces (known and unknown), most will be zero do i = 1, dof load(i) = 0.0 do j = 1, dof load(i) = load(i) + gstifforig(i, j) * disp(j)! Find stress in each member do ielem = 1, numelem cosang = cos(angrad(ielem)) sinang = sin(angrad(ielem)) i = leftnode(ielem) j = rightnode(ielem) temp = youngmod(ielem) / elemlen(ielem) stress(ielem) = temp * ( cosang*disp(2*(i 1)+1) sinang*disp(2*(i 1)+2) & + cosang*disp(2*(j 1)+1) + sinang*disp(2*(j 1)+2) ) CALL CPU_TIME(t2) write (*,"('elasped time:', E14.8)") (t2 t1)

7 C:\files\classes\fem\program code\truss\truss solve\truss.f ! Results Output to file " Results " "Global Node Displacement and Force" write (6,64) (i, load(2*(i 1)+1), disp(2*(i 1)+1), load(2*(i 1)+2), disp(2*(i 1)+2), i = 1, numnode) 64 format (" Node X Load X Disp Y Load Y Disp " / (I5, 4E12.4))! Results Output to file "Element Axial Load and Stress" write (6,75) (ielem, stress(ielem)*area(ielem), stress(ielem), ielem = 1, numelem) 75 format (" Element Load Stress " / (I7, 1E14.4, 1E14.4)) write (*,*) 'truss End' end program truss