An efficient 4‐node facet shell element for the modified couple stress elasticity

Abstract

This work proposes a simple but robust 4-node 24-DOF facet shell element for static analysis of small-scale thin shell structures. To accommodate the size effects, the modified couple stress theory is employed as the theoretical basis.The element is constructed via two main innovations. First, the trial functions that can a priori satisfy related governing differential equations are adopted as the basic functions for formulating the element interpolations. Second, the generalized conforming theory and the penalty function method are employed to meet the C 1 continuity requirement in weak sense for ensuring the computation convergence property. Several benchmarks of shells with different geometries are tested to assess the new facet shell element's capability. The numerical results reveal that the element can effectively simulate the size-dependent mechanical behaviors of small-scale thin shells, exhibiting satisfactory numerical accuracy and low susceptibility to mesh distortion. Moreover, as the shell element uses only six degrees of freedom per node, it can be incorporated into the commonly available finite element programs very readily.

A non-classical couple stress based Mindlin plate finite element framework for tuning band gaps of periodic composite micro plates

“…Chen ([17]) proposed a new set of non-classical wave equations to investigate layered phononic crystals. Based on the high-order continuum theories, several size-dependent micro beam ( [18,19]), plate ([20, 21, 22, 23]) and shell ( [24,25]) models have been recently developed to study microscopic thin structures. Among these achievements, only a few models provide numerical solution with finite element formulation.…”

“…Note that in the above expressions Eq. (25,27), G refers to shear modulus, E is Young's modulus, ν is Possion's ratio, and k 11 , k 22 are in-plane shear correction parameters, which in this article, take the following value k 11 = k 22 = 5 6 .…”

Size-dependent finite element analysis of FGMs in thermal environment based on the modified couple stress theory

“…From the above literature review, it is clear that analytical or semi-analytical solutions are often limited to simple structural forms or material distributions and typically unavailable or impractical for complex engineering problems. Therefore, numerical methods such as the finite element method (FEM) (Shang et al, 2020(Shang et al, , 2021, the isogeometric method (Liu et al, 2017), the meshless method (Jankowski et al, 2022) and the boundary element method (Rodopoulos et al, 2021) have been extensively employed to provide high precision and computational efficiency in solving these problems. Among these, the FEM has gained popularity due to its computation efficiency and simplicity in enforcing boundary conditions but it still suffers several drawbacks.…”

“…From the above literature review, it is clear that analytical or semi-analytical solutions are often limited to simple structural forms or material distributions and typically unavailable or impractical for complex engineering problems. Therefore, numerical methods such as the finite element method (FEM) (Shang et al ., 2020, 2021), the isogeometric method (Liu et al. , 2017), the meshless method (Jankowski et al.…”