# Input File for Cantilever Shear-beam

/*
*  ======================================================================
*  Finite element model of shear-beam using 4 node shell finite element.
*
*  In this example, the cantilever beam is modeled with a 8x2 irregularly
*  shaped finite element mesh.
*
*  Written By : Lanheng Jin                                  April, 1994
*  ======================================================================
*/

print "*** DEFINE PROBLEM SPECIFIC PARAMETERS \n\n";

NDimension         = 3;
NDofPerNode        = 6;
MaxNodesPerElement = 4;

/*
*  ===============
*  Define the Mesh
*  ===============
*/

StartMesh();

print "*** GENERATE GRID OF GEOMETRY FOR FE MODEL \n\n";

L   =  48 in;   /* Length     */
b   =  12 in;   /* Width      */
t   =   1 in;   /* Thickness  */

print "*** GENERATE GRID OF NODES FOR FE MODEL \n\n";

y  = 0 in;
AddNode( 1, [ 0.0 in, y, 6.0 in]);
AddNode( 2, [ 0.0 in, y, 0.0 in]);
AddNode( 3, [ 0.0 in, y,-6.0 in]);
AddNode( 4, [ 6.0 in, y, 6.0 in]);
AddNode( 5, [ 7.0 in, y, 0.0 in]);
AddNode( 6, [ 8.0 in, y,-6.0 in]);
AddNode( 7, [12.0 in, y, 6.0 in]);
AddNode( 8, [14.0 in, y, 0.0 in]);
AddNode( 9, [16.0 in, y,-6.0 in]);
AddNode(10, [18.0 in, y, 6.0 in]);
AddNode(11, [18.0 in, y, 0.0 in]);
AddNode(13, [24.0 in, y, 6.0 in]);
AddNode(14, [22.0 in, y, 0.0 in]);
AddNode(16, [30.0 in, y, 6.0 in]);
AddNode(17, [27.0 in, y, 0.0 in]);
AddNode(19, [36.0 in, y, 6.0 in]);
AddNode(20, [32.0 in, y, 0.0 in]);
AddNode(22, [42.0 in, y, 6.0 in]);
AddNode(23, [40.0 in, y, 0.0 in]);
AddNode(25, [48.0 in, y, 6.0 in]);
AddNode(26, [48.0 in, y, 0.0 in]);

print "*** ATTACH ELEMENTS TO GRID OF NODES \n\n";

nn  = 9;
for(j=1; j < nn; j=j+1) {
for(i=1; i<=2; i=i+1) {
elmtno = i+2*(j-1);
a = 3*(j-1)+i+1;
b = 3*j+i+1;
c = 3*j+i;
d = 3*(j-1)+i;
node_connec = [a, b, c, d];
}
}

/*
*  ===============================================
*  Define Element, Section and Material Properties
*  ===============================================
*/

print "*** DEFINE ELEMENT, SECTION AND MATERIAL PROPERTIES \n\n";

ElementAttr("name_of_elmt_attr") { type     = "SHELL_4NQ";
section  = "mysection";
material = "ELASTIC";
}

MaterialAttr("ELASTIC") { poisson = 0.25;
E       = 30000 ksi;
}

SectionAttr("mysection") { thickness =   1 in; }

/*
*  =========================
*  Setup Boundary Conditions
*  =========================
*/

print "*** SET UP BOUNDARY CONDITIONS \n\n";

/*  Establish array for full fixity condition  */

u_id  = 1; v_id  = 1; w_id  = 1;
rx_id = 1; ry_id = 1; rz_id = 1;
bc_fc = [u_id,v_id,w_id,rx_id,ry_id,rz_id];

/*  Apply full fixity to corner nodes  */

for (i=1; i<=3; i=i+1) {
FixNode(i, bc_fc);
}

/*
*  ==================
*  ==================
*/

print "*** APPLY EXTERNAL LOADS \n\n";

Fx = 0 lbf;    Fy = 0 lbf;    Fz = 10000 lbf;
Mx = 0 lbf*in; My = 0 lbf*in; Mz = 0 lbf*in;

NodeLoad( 25, [Fx, Fy, Fz, Mx, My, Mz]);
NodeLoad( 27, [Fx, Fy, Fz, Mx, My, Mz]);

Fx = 0 lbf;    Fy = 0 lbf;    Fz = 20000 lbf;
Mx = 0 lbf*in; My = 0 lbf*in; Mz = 0 lbf*in;

NodeLoad( 26, [Fx, Fy, Fz, Mx, My, Mz]);

/*
*  =====================================
*  Compile and Print Finite Element Mesh
*  =====================================
*/

EndMesh();
PrintMesh();

/*
*  ==========================
*  Compute Stiffness Matrices
*  ==========================
*/

print "\n*** COMPUTE STIFFNESS MATRICES \n\n";

SetUnitsType("US");
stiff  = Stiff();
lu     = Decompose(Copy(stiff));

/*
*  ================================
*  Print displacements and stresses
*  ================================
*/

PrintDispl(displ);
PrintStress(displ);

quit;

### Points to note are:

• This input file is for a cantilever shear-beam modeled with an 8x2 irregularly shaped finite element mesh.
• In Part 1 we specify that this will be a three-dimensional analysis. The maximum number of degrees of freedom per node will be six, and the maximum number of nodes per element will be four. The parameters NDimension, NDofPerNode, and MaxNodesPerElement are used by ALADDIN to assess memory requirements for the problem storage and solution.
• We generate the mesh of 27 finite element nodes and 16 elements. Before the boundary conditions are applied, the structure has 162 degrees of freedom. In boundary conditions section we apply full-fixity to the support-end of the cantilever -- this reduces degrees of freedom from 162 to 144.

Developed in June 1996 by Lanheng Jin and Mark Austin