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首页> 外文期刊>Latin American Journal of Solids and Structures >A Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations
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A Timoshenko Piezoelectric Beam Finite Element with Consistent Performance Irrespective of Geometric and Material Configurations

机译：与几何和材料配置无关的具有一致性能的Timoshenko压电梁有限元

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摘要

Abstract The conventional Timoshenko piezoelectric beam finite elements based on First-order Shear Deformation Theory (FSDT) do not maintain the accuracy and convergence consistently over the applicable range of material and geometric properties. In these elements, the inaccuracy arises due to the induced potential effects in the transverse direction and inefficiency arises due to the use of independently assumed linear polynomial interpolation of the field variables in the longitudinal direction. In this work, a novel FSDT-based piezoelectric beam finite element is proposed which is devoid of these deficiencies. A variational formulation with consistent through-thickness potential is developed. The governing equilibrium equations are used to derive the coupled field relations. These relations are used to develop a polynomial interpolation scheme which properly accommodates the bending-extension, bending-shear and induced potential couplings to produce accurate results in an efficient manner. It is noteworthy that this consistently accurate and efficient beam finite element uses the same nodal variables as of conventional FSDT formulations available in the literature. Comparison of numerical results proves the consistent accuracy and efficiency of the proposed formulation irrespective of geometric and material configurations, unlike the conventional formulations.
机译：摘要基于一阶剪切变形理论（FSDT）的常规Timoshenko压电梁有限元无法在材料和几何特性的适用范围内保持一致的精度和收敛性。在这些元素中，由于在横向方向上引起的潜在效应而导致不精确，而由于在纵向方向上使用场变量的独立假定的线性多项式插值而导致效率低下。在这项工作中，提出了一种新颖的基于FSDT的压电束有限元，它没有这些缺陷。开发了具有一致的贯穿厚度潜力的变体配方。控制平衡方程用于导出耦合场关系。这些关系用于开发多项式插值方案，该方案可以适当地适应弯曲延伸，弯曲剪切和感应电势耦合，从而以有效的方式产生准确的结果。值得一提的是，这种始终如一的精确有效的光束有限元使用的节点变量与文献中可用的常规FSDT公式相同。数值结果的比较证明，与常规配方不同，无论几何形状和材料配置如何，所提出配方的准确性和效率都是一致的。

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