A cross-section interpolation beam model considering temperature effect
PAN Chenghao1, CHEN Guoping1,2, HE Huan1,2
1.State Key Lab of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
2.Institute of Vibration Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract:A cross-section interpolation beam model was proposed to solve the dynamic and static response of the beam under nonuniform thermal load. It solved the problem that the traditional beam theory cannot deal with the beam subjected to nonuniform temperature field. Firstly, the Lagrange interpolation function was used to interpolate the section and axial of the beam element to construct the displacement field of the beam. Then, the displacement field was substituted into the thermoelastic dynamic equation, and the element strain and stress were obtained. According to the principle of virtual work, the element stiffness matrix, mass matrix and equivalent node load array were derived, and the thermal stress was solved. Finally, the element stiffness matrix was updated by the transverse shear force of thermal stress to calculate the vibration characteristics of the beam under thermal load. The calculation results showed that the results obtained by the method in this paper are consistent with the results of the solid element model, and it is easier to deal with the slender structure under non-uniform thermal load, and can well reflect the shape, load and response results of the cross section.
潘成浩1,陈国平1,2,何欢1,2. 一类考虑温度效应的截面插值梁模型[J]. 振动与冲击, 2023, 42(5): 215-222.
PAN Chenghao1, CHEN Guoping1,2, HE Huan1,2. A cross-section interpolation beam model considering temperature effect. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(5): 215-222.
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