板的自由振动和机械屈曲——一种三维一致方法
Free vibration and mechanical buckling of plates with in-plane material inhomogeneity - a three dimensional consistent approach
AI总结：
本文基于扩展边界有限元法研究板的自由振动和机械屈曲，采用二维高阶谱元建模板的平面尺寸，通过Pade展开解析求解厚度方向，直接推导三维解得到对角质量矩阵，无需剪切修正因子和数值锁固，研究材料梯度指数、边界条件和几何形状对基频和临界屈曲载荷的影响。
摘要：
本文研究了基于扩展边界有限元法的板的自由振动和机械屈曲问题。通过二维高阶谱元建模板的平面尺寸，厚度方向的解通过Pade展开解析表达。刚度矩阵直接由三维解推导得出，利用谱元方法获得对角质量矩阵。该方法无需任意剪切修正因子且不产生数值锁固。假设材料特性温度无关，仅在平面方向通过简单幂律梯度分布。有效材料特性通过混合规则估算。数值研究了材料梯度指数、边界条件和板几何形状对基频和临界屈曲载荷的影响。
英文摘要：
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by two-dimensional higher order spectral element. The solution through the thickness is expressed analytically with Pade expansion. The stiffness matrix is derived directly from the three dimensional solutions and by employing the spectral element, a diagonal mass matrix is obtained. The formulation does not require ad hoc shear correction factors and no numerical locking arises. The material properties are assumed to be temperature independent and graded only in the in-plane direction by a simple power law. The effective material properties are estimated using the rule of mixtures. The influence of the material gradient index, the boundary conditions and the geometry of the plate on the fundamental frequencies and critical buckling load are numerically investigated.
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