论文标题

实心壳棱镜元素基于分层,异质和各向异性形状函数

Solid shell prism elements based on hierarchical, heterogeneous, and anisotropic shape functions

论文作者

Kaczmarczyk, Lukasz, Nguyen, Hoang, Ullah, Zahur, Wakeni, Mebratu, Pearce, Chris

论文摘要

提出了一种新的棱镜有限元的配方,用于对固体壳的非线性分析,受到大型菌株和大型位移的影响。该元素基于分层,异质和各向异性形状函数。与其他固体壳配方一样,仅需要位移自由度来描述壳运动学,并且可以采用一般的三维物质定律。但是,这种公式的新颖性是能够捕获复杂的壳行为并避免锁定现象的能力,而无需使用减少的集成或采用其他自然应变或增强的应变场。因此,该元素理想地适合几何和物理非线性问题。这是通过在棱镜元件的三角形面上以及通过厚度构建独立的近似形状函数来实现的,而后者与局部坐标系相关联,该系统与壳变形相关。该元素非常有效,层次属性将其本身用于有效且高度可扩展的多机求解器,而异质性属性可以实现局部P-适应性。本文证明了该元素在许多线性和几何非线性问题方面的性能,这是针对文献中确定的问题的基准测试的。该公式已在MOFEM中实现。

The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As with other solid shell formulations, only displacement degrees of freedom are required to describe the shell kinematics and general three-dimensional material laws can be adopted. However, the novelty of this formulation is the ability to capture complex shell behaviour and avoid locking phenomena, without the need to use reduced integration or adopt additional natural strain or enhanced strain fields. Thus, this element is ideally suited for geometrically and physically nonlinear problems. This is achieved by constructing independent approximation shape functions on both the prism element's triangular faces and through the thickness, where the latter is associated with a local coordinate system that convects with deformation of the shell. The element is extremely efficient, with the hierarchical property lending itself to an efficient and highly scalable multigrid solver, and the heterogeneity property enables local p-adaptivity. The paper demonstrates performance of the element for a number of linear and geometrically nonlinear problems, benchmarked against well established problems in the literature. The formulation has been implemented in the MoFEM.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源