This paper describes an eight-node, assumed strain, solid-shell, corotational element for geometrically nonlinear structural analysis. The locally linear kinematics of the element is separated into in-plane (which is further decoupled into membrane and bending), thickness and transverse shear components. This separation allows using any type of membrane quadrilateral formulation for the in-plane response. Assumed strain fields for the three components are constructed using different approaches. The Assumed Natural Deviatoric Strain approach is used for the in-plane response, whereas the Assumed Natural Strain approach is used for the thickness and transverse shear components. A strain enhancement based on Enhanced Assumed Strain concepts is also used for the thickness component. The resulting element passes well-known shell element patch tests and exhibits good performance in a number of challenging benchmark tests. The formulation is extended to the geometric nonlinear regime using an element-independent corotational approach. Some key properties of the corotational kinematic description are discussed. The element is tested in several well-known shell benchmarks and compared with other thin-shell and solid-shell elements available in the literature, as well as with commercial nonlinear FEM codes. 146M. MOSTAFA, M. V. SIVASELVAN AND C. A. FELIPPA and degenerate shell formulations. A paradigm for thin-shell elements that falls outside the aforementioned three categories is based on the concept of subdivision surfaces [14,15] and has been found to outperform traditional formulations.In this paper, a solid-shell formulation is developed using an assumed strain approach. Attractive features of a solid-shell element include the following.Modeling simplifications that result from avoiding 3D rotational DOF (in fact, this work was motivated by a model reduction application, in which the element configuration space with only translational DOF has a simpler vector space structure). Realistic representation of 3D boundary conditions without need for additional kinematic assumptions. For example, distinctions can be made as to whether supports are applied to the top or bottom surface. Simplified coupling with standard solid elements without multifreedom constraints. This coupling may be necessary when smooth shell structures interact with features that require a more detailed 3D treatment, such as folds, edge reinforcements or mushroom slab supports.Examples of early work on solid-shell elements are addressed in [16][17][18][19]. Sze [20] discussed the different challenges that arise in solid-shell element development and strategies that have been developed to address them. Schwarze and Reese [21] present a comprehensive survey of different solid-shell element formulations.In modeling shell structures, the well-known displacement-based approach used in conventional solid elements is not rich enough to capture kinematics associated with bending normal to the shell surface. As a result, solid-shell elements are susceptible to...

SUMMARY We discuss a strategy to construct corotated frames for three‐dimensional continuum finite elements by minimizing deformations within the frame. We find that irrespective of the type of element and the number of nodes, using a quaternion parametrization of rotations, this minimization is naturally stated as computing the smallest eigenvalue of a 4 × 4 matrix. The simplicity of this smallest eigenvalue plays a crucial role when linearizing the kinematics. Ensuant quaternion algebra, although lengthy, results in remarkably simple formulas for projections that arise in the linearized kinematics. The exact stiffness matrix does not require computation of the second derivative of the rotation function and is also given by a simple formula. As a result, the implementation of this corotational formulation becomes particularly straightforward. Furthermore, in contrast to other results in the literature, the stiffness matrix for elements with translational DOFs is symmetric. For illustration, this corotational formulation is applied to a solid‐shell finite element, and numerical results are presented. Copyright © 2014 John Wiley & Sons, Ltd.

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SUMMARYThis paper presents an eight-node nonlinear solid-shell element for static problems. The main goal of this work is to develop a solid-shell formulation with improved membrane response compared with the previous solid-shell element (MOS2013), presented in [1]. Assumed natural strain concept is implemented to account for the transverse shear and thickness strains to circumvent the curvature thickness and transverse shear locking problems. The enhanced assumed strain approach based on the Hu-Washizu variational principle with six enhanced assumed strain degrees of freedom is applied. Five extra degrees of freedom are applied on the in-plane strains to improve the membrane response and one on the thickness strain to alleviate the volumetric and Poisson's thickness locking problems. The ensuing element performs well in both in-plane and out-of-plane responses, besides the simplicity of implementation. The element formulation yields exact solutions for both the membrane and bending patch tests. The formulation is extended to the geometrically nonlinear regime using the corotational approach, explained in [2]. Numerical results from benchmarks show the robustness of the formulation in geometrically linear and nonlinear problems.

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