Abstract This paper introduces the inverse finite element method using simple brick elements that can be used for shell analysis. The proposed element is the inverse counterpart of an existing Lagrangean-based “direct” trilinear hexahedral finite element that uses the approaches of reduced integration, assumed natural strains and enhanced assumed strain to prevent locking defects in shell modeling. Like the standard trilinear hexahedral element, this locking-free element has eight vertex nodes and three displacement degrees-of-freedom per node. It also has one scalar enhanced-strain degree-of-freedom, which is eliminated at the element level. Both inverse and direct finite element formulations are identical up to the definition of the Lagrangean-based equilibrium equations. For the inverse approach, these equations have as unknowns the positions of the nodes in the undeformed configuration. The current approach is particularly well suited for a category of inverse problems where a given shape must be attained after large elastic deformations. This is the case in the design of turbine blades, to be developed here.

中文翻译：

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使用简单的简化积分六面体实体壳单元进行逆有限元分析

摘要 本文介绍了使用可用于壳分析的简单砖单元的逆有限元方法。提议的元素是现有的基于拉格朗日的“直接”三线性六面体有限元的逆对应物，它使用减少积分、假设自然应变和增强假设应变的方法来防止壳建模中的锁定缺陷。与标准三线性六面体单元一样，这种无锁定单元具有八个顶点节点和每个节点三个位移自由度。它还具有一个标量增强应变自由度，它在元素级别被消除。根据拉格朗日平衡方程的定义，逆有限元公式和直接有限元公式是相同的。对于逆方法，这些方程将未变形配置中节点的位置作为未知数。当前的方法特别适用于一类逆问题，其中必须在大的弹性变形后获得给定的形状。涡轮叶片的设计就是这种情况，将在这里开发。