An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates
An enhanced single-layer variational formulation for the effect of transverse shear on laminated orthotropic plates
复制标题
层合正交各向异性板横向剪切效应的增强单层变分公式
DOI：
10.1016/j.euromechsol.2009.12.004
复制
发表时间：
2010
影响因子：
4.1
通讯作者：
P. Weaver
中科院分区：
文献类型：
--
作者：
E. Cosentino;P. Weaver
利用基于Castigliano最小功原理的Reissner变分法，结合拉格朗日变分法，导出了一种新的混合公式。控制方程为用二维形式模拟板的重要三维结构方面提供了另一种理论。通过对厚度坐标的经典柯西平衡方程进行积分，并在每层界面处强制剪应力和法向应力的连续性，浓缩了厚度的影响。本文还提出了一种包含微分修正因子的六阶一元偏微分方程简化系统，对复合材料层合板的经典本构方程进行了正式修正。该理论退化为薄结构的经典复合板分析。当厚度与平面内尺寸相当时，观察到与经典板理论的显著偏差。提出了各种案例研究，并将解决方案与文献中可用的其他模型和有限元分析进行了比较。
A novel mixed formulation is derived by means of Reissner's variational approach-based on Castigliano's principle of least work in conjunction with a Lagrange multiplier method for the calculus of variations. The governing equations present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. A reduced system of partial differential equations of sixth-order in one variable, is also proposed, which contains differential correction factors that formally modify the classical constitutive equations for composite laminates. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions. A variety of case studies are presented and solutions are compared with other models available in the literature and with finite element analysis.