This paper is concerned with the formulation and solution technique of the geometrically nonlinear truss system with multi-freedom constraints under simultaneously mechanical and thermal load based on the mixed finite element formulation. For geometrically nonlinear analysis of truss with multi-freedom constraint under thermal load based on displacement-based finite element formulation, it is required to incorporate the temperature variation as a dependent boundary constraint and the multi-freedom constraints to the master stiffness equation for producing a modified system of equation. To overcome the difficulties of incorporation of temperature variation, in this research, the novel mixed finite truss element with temperature variation considering geometric non-linearity is constructed based on finite element formulation. Utilizing the proposed mixed truss element, the mixed equilibrium equation of the truss system is built according to the principle of stationary potential energy. The author proposes using the Lagrange multipliers method to convert a constrained problem into an unconstrained problem for incorporating multi-freedom constraints into the established mixed finite element equilibrium equation. The incremental-iterative algorithm for solving a nonlinear system of equations is established using the arc-length method. The incremental-iterative algorithm is used to write a calculation program for geometrically nonlinear analysis of truss systems with multi-freedom constraints under mechanical and thermal load
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