Thermal-mode Analysis Of Thermal-gradient Beam And Plate Element

Thermal deformation and thermal modal analysis are important parts of structural analysis.Traditional beam and plate elements can only deal with the influence of in-plane temperature gradientupon deformation and modal, rather than through-thickness temperature gradient. In order to analyzethe influence of through-thickness temperature gradient, relative research is carried on in this paper.1. Introduction of FEM of temperature and thermal stress field. Thermal deformation problemscan be transformed into elastic ones once in-plane and through-thickness temperature isequivalent to thermal load.2. Introduction to geometric stiffness matrix of beam and plate under small deformation. Thermalmatrix equals linear matrix and geometric stiffness matrix, which fulfills the FEM of thermalmodal and thermal vibration.3. Assume the linear distribution of temperature through thickness, and split it into symmetricaland anti-symmetrical parts. And then use plane stress and blending elements respectively tocalculate relative in-plane and blending thermal loads. By addition of them, derives thedeformation. Comparison between the result and that of Nastran’s3d elements shows gooddeformation accuracy. If high temperature’s influence upon E is taken into consideration,deformation changes little.4. Traditional beam and shell element can only reflect the influence of in-plane stress uponstiffness. In order to study the influence of through-thickness temperature upon stiffness andmodal, more complete geometric stiffness matrix is derived on the base of Green-Strain.Comparison between the result and that of Nastran’s3d elements shows better deformationaccuracy than that of traditional elements. If high temperature’s influence upon E is taken intoconsideration, modal changes much.5. A project case. This chapter carries on modal and acceleration analysis of an Al-Mg alloyvibration table. The result shows that large temperature significantly reduces vibration table’slow frequency and largely weakens its effective working frequency. If high temperature’sinfluence upon E is taken into consideration, modal as well as acceleration changes obviously.