2D TRUSS FINITE ELEMENT W/ MULTI-POINT BOUNDARY CONDITIONS

This script solves the displacements, reactions, strains and stresses of a 2D truss structure using the finite element penalty approach.

The formulation is for 2-noded elements with first order linear shape functions. Each global node has 2 degrees-of-freedom - one in the x-direction and one in the y-direction. The system of linear equations (SLE) is solved for by using the finite element analysis penalty approach. This code has support for multi-point boundary conditions in the global coordinate system, such as an inclined roller support. Please see attached .pdf document for a description of this implementation).

The "preprocessor" section is based on an example 2-element truss system (please see image). A user is required to input the following truss information: node ID, degree-of-freedom (dof) indices, nodal coordinates, element ID, element end-node IDs, element cross-section, element Young's modulus, boundary conditions (i.e., support conditions), applied forces, a constant to modify the SLE with, as per the penalty approach, and finally, a description of their multi-point boundary condition (if any, this is not required).

A user must follow the general input format I used here. All inputs are defined in the "preprocessor" section and there should be no need to modify anything under the "generic algorithm" section (unless you want to). The algorithm should generally work for any simple 2D truss configuration.