Combined Torsion of FGM Triangular Section Beams Based on the"Plate-Beam"Theory
Triangular section beams have been widely used in the engineering field due to their excellent mechanical properties.Functionally gradient materials(FGMs)also exhibit excellent performance and broad application prospects due to their ability to design materials with unidirectional or bidirectional changes in material properties based on material functionality.Taking the case of a triangular section cantilever beam with FGM properties varying along the width of the plate as an example,when subjected to a concentrated torque at the end,the total potential energy and total strain energy expressions for the combined torsion of the cantilever beam were derived based on the"plate-beam"theory and relevant assumptions.The warping stiffness and free torsional stiffness of the triangular section were provided,and an energy variational model was established,and according to the principle of energy variation,an energy differential model was further obtained.The expression for the maximum torsion angle of a triangular section cantilever beam under the action of end torque was finally solved.A corresponding finite element model was established using the finite element software ANSYS and solved.The finite element results were compared with the theoretical results,and the correctness of the"plate-beam"theory was verified.
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