几何非线性固体壳单元新列式的研究

通过定义广义应力，提出了一个改进的刚度矩阵，以克服固体壳元的厚度自锁问题；由一个基于广义应力的新的非线性变分泛函，推导了一个用于几何非线性分析的十八节点固体壳单元，精心选择低、高阶应力插值模式，保证二者正交，且对应于低阶项的刚度阵与减缩积分单元相当，对应高阶项的刚度阵用于克服单元的零能模式且可推得显式，从而显著提高了计算效率，此外该单元还拥有优秀的收敛性能，即使在非常大的载荷步下也能取得好的收敛结果。

Novel Formulation of Solid Shell Element for Geometrically Nonlinear Analysis

By defining generalized stress, a modified stiffness matrix is used to overcome the thickness locking of solid shell element. Based on the generalized stress, a new nonlinear variational principle is advised and a 18 node solid shell element is derived for the geometrically nonlinear analysis. The higher order stress modes pertinent to the stabilization are contravariant in nature and their energy products with the displacement derived covariant strain can be programmed without resorting to numerical integration and Gram Schmidt orthogonalization, moreover, the higher order stress modes are judiciously selected to vanish at the sampling points of the second order quadrature. By assuming a trilinear distribution of the acquired Cauchy stress, the residual force terms turn out to be similar as that of uniformly reduced integration (URI) element. Accuracy of the element is virtually identical to that of the URI element, yet a little additional computational costs for stabilization matrix can guarantee it free from commutable zero energy modes. The element has excellent convergence behaviors, and can obtain good convergence results even using larger load steps.