正交各向异性材料的三维弹塑性分析

本文根据Hill屈服准则以张量形式推导出正交各向异性材料的弹塑性刚度,并进而导出在三维和二维情况下对应的弹塑性刚度矩阵的显表达式。所得到的公式在形式上与各向同性材料的弹塑性刚度矩阵十分类似。所以。根据本文的公式,用有限元求解时,就能很方便地将现有的各向同性体弹塑性分析的实用程序改换为正交各向异性体弹塑性分析的实用程序。作为例子,选择了一个非线性有限元通用程序,用本文公式在其三维元素的材料库中建立了新模块,并就三维悬臂梁进行了计算。

3-D ELASTO-PLASTIC ANALYSIS OF ORTHOGONAL ANISOTROPIC MATERIALS

This paper derives tensor formula of elastoplastic stiffness for orthogonal anisotropic materials based on Hill's yield criterion and gives the corresponding explicit expressions for elasto-plastic stiffness matrices in 2-D and 3-D cases, The form of the obtained matrices are quite similar to that for isotropic materials. Therefore, when using F E M to. solve Problems, an existing program for isotropic materials can easily. be modified to include orthogonal anisotropic analysis. As an example, a general purpose nonlinear F E M program is chosen and a material library model is added and, finally, a 3-D cantilever beam is evaluated.