Abstract
A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis. The smoothing process is successfully performed on the element mid-surface to deal with the membrane and bending effects of the stiffness matrix. The strain smoothing process allows replacing the Cartesian derivatives of shape functions by the product of shape functions with normal vectors to the element mid-surface boundaries. The present formulation remains competitive when compared to the classical finite element formulations since no inverse of the Jacobian matrix is calculated. The three dimensional resultant shell theory allows the element kinematics to be defined only with the displacement degrees of freedom. The assumed natural strain method is used not only to eliminate the transverse shear locking problem encountered in thin-walled structures, but also to reduce trapezoidal effects. The efficiency of the present element is presented and compared with that of standard solid-shell elements through various benchmark problems including some with highly distorted meshes.
Highlights
A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis
Several 3D numerical benchmark problems have been used as evaluation tools, revealing the efficiency of the smoothed finite element method (SFEM), when compared to the classical finite element method (FEM) in membrane and bending problems
In accordance with Theorem 3 of Liu et al [36], it is observed that the solution obtained with SFEM elements will approach the standard compatible displacement FEM model when the number a smoothing cells increases
Summary
Abstract A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis. A key point of their work is the smoothing of the assumed shear strain of the MITC4 element using the edge-based strain smoothing method presented in Liu et al [51] Their proposed element shows improved results accuracy, especially in cases of a highly distorted mesh. To the best of our knowledge, the following issues are either scarce or did not receive much attention: (i) a full assessment of the theoretical basis of the stabilization techniques proposed in Nguyen-Xuan [52] and Bordas et al [53]; (ii) the performance of the eight-node solid element using the SFEM in case of a distorted mesh; (iii) application of SFEM shell elements formulation to geometric and material non-linear problems; (iv) implementation of the SFEM approach in solid-shell elements.
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