实体退化板单元及其在板的振动分析中的应用

经典板壳单元是由板壳理论构造出来的,而经典的板壳理论是在空间弹性理论的基础上考虑板壳的基本假定得来的。在空间等参数单元的基础上,直接引入板壳的基本假定,修改空间等参数单元的弹性矩阵,从而构造出适合于厚薄板壳分析的20结点实体退化板单元,并将其应用于开口圆柱薄壳的静力分析和厚薄板的固有振动分析。数值算例表明,该单元收敛快,稳定性好,具有较高的精度。此外,该单元还可以用于曲边变厚度板、壳体及层合板的振动分析。

DEGENERATED SOLID PLATE ELEMENT AND ITS APPLICATION TO VIBRATION ANALYSIS OF PLATES

Classical plate and shell finite elements are derived from corresponding theories of plate and shell, and the theories of plate and shell are based on spatial theory of elasticity and plate-shell assumptions. In this paper, the fundamental plate and shell assumptions are directly introduced into the 20-node spatial isoparametric finite element. By modifying the elastic matrix of the spatial isoparametric finite element, one new plate element suitable for analysis of thick and thin plates and shells 20-node degenerated solid plate element, is developed. The degenerated solid plate element is used in static analysis of one open cylindrical thin shell and the natural vibration analysis of thick and thin plates. Numerical results show that the degenerated solid plate element has the advantages of good convergence, stability and higher precision. Moreover, the element can also be used to analyze the vibration of curved plates with variable thickness, laminated plates and shells.