Airy stress function for proposed thermoelastic triangular elements

This study aims to improve the performance of thermoelastic triangular elements. New triangular elements are proposed with different degrees of freedom. Plane stress models are developed to simulate the complex evolution of structures under external force and thermal conditions. First of all, the structure is analyzed based on the established complementary energy function. In this scheme, the Airy stress function is implemented. The performances of plane stress problems are found by a type of analytical solution. Consequently, the obtained equations are rewritten in terms of the nodal values. After suggesting new elements, extensive analyses for the plane stress problems were performed, and the numerical studies validated the proper behavior of the novel elements. The obtained results clearly showed that the new procedure led to precisions of structural deformation and stresses. In this investigation, different benchmarks, such as small patches, cantilever beams, thick curved beams, non-prismatic cantilever beams, and thin plates, were evaluated. Problems are solved under different loading conditions, including mechanical load, thermal load, and a combination of mechanical–thermal loads. The analytical trial function approach for the construction of an eight-node plane element is used because the formulations are identical. This study helps to find the near-exact values of different responses under the influence of thermal load in addition to external loading, including both displacement and stress outcomes.