A cross-section interpolation beam model considering temperature effect

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (5) : 215-222.

PAN Chenghao1, CHEN Guoping1,2, HE Huan1,2

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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.

Key words

spatial beam model / cross-section interpolations / cross-section deformation / static calculation / thermal modal analysis

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PAN Chenghao1, CHEN Guoping1,2, HE Huan1,2. A cross-section interpolation beam model considering temperature effect[J]. Journal of Vibration and Shock, 2023, 42(5): 215-222

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