This paper investigates the capacity of solid finite elements with independent interpolations for displacements and strains to address shear, membrane and volumetric locking in the analysis of beam, plate and shell structures. The performance of the proposed strain/displacement formulation is compared to the standard one through a set of eleven benchmark problems. In addition to the relative performance of both finite element formulations, the paper studies the effect of discretization and material characteristics. The first refers to different solid element typologies (hexahedra, prisms) and shapes (regular, skewed, warped configurations). The second refers to isotropic, orthotropic and layered materials, and nearly incompressible states. For the analysis of nearly incompressible cases, the B-bar method is employed in both standard and strain/displacement formulations. Numerical results show the enhanced accuracy of the proposed strain/displacement formulation in predicting stresses and displacements, as well as producing locking-free discrete solutions, which converge asymptotically to the corresponding continuous problems.

本文研究了在分析梁，板和壳结构时，具有独立插值法的实体有限元的位移和应变能力，以解决剪切，膜和体积锁定问题。通过一组十一个基准问题，将拟议的应变/位移公式的性能与标准公式进行了比较。除了两种有限元公式的相对性能外，本文还研究了离散化和材料特性的影响。第一种是指不同的实体元素类型（六面体，棱柱形）和形状（规则，偏斜，翘曲的配置）。第二种是指各向同性，正交各向异性和层状材料以及几乎不可压缩的状态。为了分析几乎不可压缩的情况，在标准配方和应变/位移配方中都使用了B型杆法。数值结果表明，所提出的应变/位移公式在预测应力和位移以及产生无锁定离散解的过程中具有更高的精度，这些离散解渐近收敛于相应的连续问题。