Abstract
A family of prismatic and hexahedral solid‒shell (SHB) elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact). Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.
Highlights
Nowadays, thin structures are increasingly used in engineering applications, and especially in automotive industries
The results reveal that both the peak and the period of the response are well predicted using the proposed SHB elements as well as ABAQUS linear shell elements, while the solution yielded by the ABAQUS linear solid elements is found far from the reference solution during the second half-period
In the formulation of the SHB elements, several local frames have been defined and used in their numerical implementation. Taking advantage of such modularity, various constitutive models have been coupled with these SHB elements, including isotropic behavior, orthotropic elastic behavior for laminated composite materials, and anisotropic plastic behavior for metallic materials
Summary
Thin structures are increasingly used in engineering applications, and especially in automotive industries. Due to the large aspect ratio (length to thickness) of thin structures, the conventional solid and shell elements suffer from various locking phenomena both in linear and nonlinear analyses. In order to obtain accurate and reliable numerical results, much effort has been dedicated in recent decades to the development of efficient locking-free finite elements. The recent concept of solid‒shell elements attracted much attention due to their outstanding advantages compared to traditional solid and shell elements. They are based on a fully three-dimensional (3D) formulation with only displacements as degrees of freedom. Combined with the reduced-integration technique, various methods have been proposed in the literature to eliminate most locking phenomena [1,2,3,4,5,6,7,8,9], among which the assumedstrain method (ASM), the enhanced assumed strain (EAS) formulation, and the assumed natural strain (ANS) approach
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