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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Evaluation and verification of an HSDT-Layerwise generalized finite element formulation for adaptive piezoelectric laminated plates
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Evaluation and verification of an HSDT-Layerwise generalized finite element formulation for adaptive piezoelectric laminated plates

机译：自适应压电叠层板HSDT分层广义有限元公式的评估与验证

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摘要

A formulation for the bending analysis of composite laminated plates with piezoelectric layers is implemented using the generalized finite element method. This formulation is derived from a mechanical description based on Higher-Order Shear Deformation Theory which allows for the use of C° continuous approximation functions on the domain. On the other hand, a Layerwise Theory is employed for interpolation of electric potential across the thickness of piezoelectric layers, in such a way that the kinematical hypotheses result in a mixed model. The paper presents an analysis of the approximation capability of the proposed numerical model for static analysis, using C~0 continuous Partition of Unity and polynomial enrichments to span the approximation spaces, by assessment of convergence. Analytical solutions obtained from the same kinematical hypotheses are used as references. Results for relative error in the energy norm considering p- and ft-refinements for regular and distorted meshes, in addition to a point-wise evaluation of the stresses and electric field, are presented. The evaluations show that the numerical methodology is a very effective tool for improving the solution through the enrichment, even for point-wise values across the thickness, and is robust to mesh distortions. Moreover, the results furnish insight about the physical modeling for both active and sensory modes, for thick and thin plates.
机译：使用广义有限元方法，实现了具有压电层的复合层压板弯曲分析的公式。该公式源自基于高阶剪切变形理论的机械描述，该理论允许在域上使用C°连续逼近函数。另一方面，采用分层理论在压电层的整个厚度上进行电势插值，以使运动学假说产生混合模型。本文通过对收敛性的评估，使用C〜0的Unity连续分区和多项式充实来跨越近似空间，对所提出的静态分析数值模型的近似能力进行了分析。从相同的运动学假设获得的解析解将用作参考。除了对应力和电场进行逐点评估外，还提出了考虑规则和变形网格的p和ft细化的能量范数的相对误差结果。评估表明，数值方法学是一种非常有效的工具，可以通过浓缩来提高求解效果，即使是沿厚度方向的逐点取值，也可以抵抗网格变形。此外，结果提供了有关厚板和薄板主动模式和感官模式的物理建模的见解。

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