摘要
复合材料夹层壳是航空航天领域中重要的结构,但它的理论特别是非线性理论还需要进一步发展,才能满足工程应用的要求。本文根据能量误差一致原则和量阶分析方法,利用Lagrange描述法首先得到复合材料夹层壳的一致有效Green应变张量,协调方程和第二Piola-Kirchhoff应力张量。据此和几个基本假设进一步获得了复合材料夹层壳的内力、内力矩的本构方程。应变能密度函数和位能泛函。再利用最小位能原理,得到了平衡方程和边界条件。这些方程在小应变,中/小转动一阶近似的意义上是一致有效的。 根据Koiter伪扁壳概念,对已获得的方程作进一步的近似处理和推导,本文最后获得复合材料夹层伪扁壳的Donnell型方程。
Cylindrical composite sandwich shells are the important structures in aeronautical and astronautical industry. The theory,especially nonlinear theory,of then is still required to be further developed so as to meet the demand of engineering application. With Lagrangian description,the consistent Green strain tensor,the compatibility equations and the second Piola-Kirchhoff stress tensor of the composite sanduich shells were successively obtained. Based on these results and several assumptions,the constitutive equations related to the stress resultents and the strains,the strain energy density and the potential energy func-tional are further developed. In terms of minimum potential energy principle,the equilibri-um equations and associated boundary conditions are derived,which are consistent in the meaning of the first order approximation under the condition of small strain accompanied with moderate / small rotation.
关键词
复合材料
夹层构件
壳体结构
composite materials,sandwich component,shell structures, non-linear theory, tensor analysis
