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In this article, a pseudo-stress for local residual and an algebraically derived consistent tangent are applied to elastic–plastic boundary value problems of shells. The authors define a coupled problem of the weak form of the equilibrium equation for the overall structure and the constrained equations for stress state, which include the yield condition and the plane stress condition, at every material point. Since the pseudo-stress for the residuals of yield criterion and plane stress state is incorporated into the linearized weak form of the equilibrium equation, the proposed scheme does not have any local iterative calculations and enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples using shell elements demonstrate the validity and effectiveness of the procedures in complex situation with material and geometrical nonlinearities. [ABSTRACT FROM AUTHOR]

In this article, an introduction of pseudo-stress for local residual and an algebraic derivation of consistent tangent are presented. The authors define a coupled problem of the equilibrium equation for the overall structure and the constrained equations for stress state at every material point, and the pseudo-stress and the derived consistent tangent can be implemented easily to finite element analysis. In the proposed block Newton method, the internal variables are also updated algebraically without any local iterative calculations. In addition, the authors demonstrate the performance of the proposed approach for both J 2 plasticity and J 2 plasticity under plane stress state. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure to couple shell to solid elements by using the Nitsche's method. The continuity of displacements can be satisfied approximately with the penalty method, which is effective in setting the penalty parameter to a sufficiently large value. When the continuity of only displacements on the interface is applied between shell and solid elements, an unreasonable deformation may be observed near the interface. In this work, the continuity of the stress vector on the interface is considered by employing the Nitsche's method, and hence a reasonable deformation can be obtained on the interface. The authors propose two types of shell elements coupled with solid elements in this paper. One of them is the conventional MITC4 shell element, which is one of the most popular elements in engineering applications. This approach shows the capability of discretizing the domain of the structure with the different types of elements. The other is the shell element with additional degrees of freedom to represent thickness-stretch developed by the authors. In this approach, the continuity of displacements including the deformation in the thickness direction on the interface can be considered. Several numerical examples are presented to examine the fundamental performance of the proposed procedure. The behavior of the proposed simulation model is compared with that of the whole domain discretized with only solid elements. [ABSTRACT FROM AUTHOR]

This paper presents a quadrilateral shell element incorporating thickness-stretch, and demonstrates its performance in small and large deformation analyses for hyperelastic material and elastoplastic models. In terms of geometry, the proposed shell element is based on the formulation of the MITC4 shell element, with additional degrees of freedom to represent thickness-stretch. To consider the change in thickness, we introduce a displacement variation to the MITC4 shell element, in the thickness direction. After the thickness direction is expressed in terms of the director vectors that are defined at each midsurface node, additional nodes are placed along the thickness direction from the bottom surface to the top surface. The thickness-stretch is described by the movement of these additional nodes. The additional degrees of freedom are used to compute the transverse normal strain without assuming the plane stress condition. Hence, the three dimensional constitutive equation can be employed in the proposed formulation without any modification. By virtue of not imposing the plane stress condition, the surface traction is evaluated at the surface where the traction is applied, whereas it is assessed at the midsurface for conventional shell elements. Several numerical examples are presented to examine the fundamental performance of the proposed shell element. In particular, the proposed approach is capable of evaluating the change in thickness and the stress distribution when the effect of the surface traction is included. The behavior of the proposed shell element is compared with that of solid elements. [ABSTRACT FROM AUTHOR]