中厚板理论的适用范围和精确程度的研究

利用Reissner中厚板理论边界元、Mindlin中厚板理论有限元和三维弹性力学有限元分析了各种厚跨比的板的位移和应力,以确定利用三维理论、中厚板理论和薄板理论分析板时厚跨比的适用范围以及精确程度,为分析板时选择采用薄板理论、中厚板理论还是三维理论提供理论依据;同时也验证了采用缩减积分的Mindlin中厚板理论有限元法缓解了剪切锁死现象.

Research on the Applicable Range and Accuracy of Moderately Thick Plate Theory

The displacements and stresses for various thickness-to-span ratios were obtained using the boundary element method(BEM) for Reissner’s moderately thick plates,and the finite element method(FEM) for Mindlin’s moderately thick plates and three dimensional problems.The applicable range and accuracy among the three dimensional theories,the moderately thick plate theory and thin plate theory were defined.A theory basis and reference for choosing the thin plate theory,the thick plate theory or the three dimensional theory to analyze plates were provided.The results have shown that shear locking is deleted when the reduced integration is used in the finite element of plates and shells.