Mixed FEM for Geometrically Nonlinear Analysis of Truss System with Multi-freedom Constraints Subjected to Mechanical and Thermal Load

The paper focuses on the formulation and solving technique of trusses with multi-freedom constraints loaded mechanically and thermally considering geometrically nonlinearity utilizing FEM with mixed primary unknown variable choice. For analysis of truss with dependent boundary conditions under thermal load using displacement-based FEM considering large displacement, it is needed to incorporate the expansion due to temperature change varying with the element’s length and the boundary relations of constraints to the FE stiffness equation for constructing the modified system of equations. To skip the incorporation process of temperature variation, in this research, a novel mixed form of finite truss element with temperature variation considering geometric non-linearity is established according to the mixed-based formulation. Utilizing the novel established element, the global equilibrium equation is built for the truss system according to the minimum total potential energy principle. The incorporation of multi-freedom constraints is done by using the Lagrange multipliers method to convert the boundary constraints. The mathematical technique based on the arc-length method has been implemented to establish an algorithm for solving a system of FEM nonlinear equations. Utilizing the incremental-iterative solution procedure established by the arc-length technique, the Matlab calculation program has been written to examine the buckling response of truss systems having boundary constraints under the action of simultaneous mechanical and thermal load.