Finite Element Verification And Combined Torsion And Vibration Theory Of Functionally Graded Material Triangular Section Beam Based On Plate-beam Theory

Torsion and shear resistance are excellent in the closed section beam.At present,most research on the closed section beam focuses on the box beam,with little focus on the torsion of the triangular thin-walled section beam.Furthermore,as a novel type of composite material,the material properties of Functionally Gradient Materials(FGM)exhibit continuous gradient changes,resulting in broad application fields and low residual stress between layers.Currently,research on FGM beam members in the field of construction engineering is becoming increasingly popular.The combined torsion,torsional vibration,and flexural-torsional vibration of functionally graded material triangular cross-section beams are theoreticcally studied in this paper using plate-beam theory.The main contents are as follows:(1)Consideing two distribution cases of functionally graded materials,i.e.,the material properties change along the thickness and width of the plate,the strain energy of the torsion deformation of the triangular thin-walled section beam is calculated using plate-beam theory.The warping moment of inertia I_w,free torsion constant J_k,and strain energy correction coefficient of functionally graded materials are calculated while taking the effect of modulus change into account.Furthermore,the expression of the maximum torsion angle of the triangular section cantilever beam is obtained.Finally,using the finite element software ANSYS,the corresponding numerical model is established,and the maximum torsion angles of triangular cantilever beams with different sizes are calculated.When the finite element results are compared to the theoretical results,the errors of the two types of FGM are between 2.77%-4.29%and 0.62%-3.10%,respectively,proving the numerical simulation’s accuracy.(2)The kinetic energy of the free torsional vibration and the free bending-torsional vibration of the triangular section beam are derived from obtaining the torsional strain energy of the triangular section beam using plate-beam theory.The polar moment of inertia I_p of the triangular section beam,as well as the kinetic energy correction coefficient,are calculated taking into account the effect of the functional gradient material modulus change.Finally,the triangular section simply supported beam’s torsional vibration frequency expression and bending-torsional vibration frequency expression are obtained.The corresponding numerical model of the triangular section simply supported beam is established using The finite element program ANSYS,and the torsional vibration frequency,as well as the bending-torsional vibration frequency,are solved.The outcomes are compared to the theoretical outcomes.The torsional vibration frequency error of the two types of functionally gradient materials is 0.8%-3.5%and 2.0%-5.3%,and the bending-torsional vibration frequency error is 4.3%-8.7%and 2.7%-7.0%,confirming the accuracy of the numerical simulation.