Thanh Chau-Dinh

Predicting residual strength of multi-cracked thin sheet plates based on CTOA or cohesive crack model using the extended finite element method

An extended finite element method is applied to predict residual strength of cracked thin sheet plates. Two kinds of middle tension M(T) testings different in initial crack direction are simulated for stable crack growth process based on a crack tip opening angle criterion or a cohesive crack model. Crack growth direction is determined from direction of the maximum principal stress at the crack tip. Material follows plane-stress J2 plasticity with linear isotropic/kinematic hardening. The residual strength and crack propagation path obtained by the extended finite element method are compared to experimental measurement and show reasonable agreement.

Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures

This paper improves four-node quadrilateral plate elements by using cell-based strain smoothing enhancement and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of composite structures. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of four-node quadrilateral plate elements that have strain components smoothed or averaged over the sub-domains of the elements. From the divergence theory, the displacement gradients in the smoothed strains are transformed from the area integral into the line one. The behavior of composite structures follows the third-order shear deformation theory. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these composite structures.

Nonlinear Static Bending Analysis of Functionally Graded Plates Using MISQ24 Elements with Drilling Rotations

This paper develops a computational model for nonlinear static bending analysis of functionally graded (FG) plates using a smoothed four-node quadrilateral element MISQ24 [1, 2] within the context of the first-order shear deformation theory (FSDT). In particular, the construction of the nonlinear geometric equations is based on Total Lagrangian approach in which motion at the present state compared with the initial state is considered large. Small strain–large displacement theory of von Karman will be used in nonlinear formulations of the smoothed quadrilateral element MISQ24 with drilling rotations. The drilling rotations are introduced to improve the coarse mesh accuracy of the MISQ24 element. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these structures.

A Node-Based MITC3 Element for Analyses of Laminated Composite Plates Using the Higher-Order Shear Deformation Theory

In this paper, the node-based smoothed finite element method is developed for three-node triangular plate elements using the mixed interpolation of tensorial components (MITC) technique to remove the shear locking. The C 0-type continuous plate elements represent the higher-order shear deformation theory of laminated composite plates by adding two degree of freedoms related to derivatives of deflection. Based on the MITC3 technique for three-node triangular degenerated shell elements, an explicit formulation of gradients of the transverse shear strains is derived. The constant strain fields within the C 0-type continuous plate elements are averaged over node-based domains defined by connecting the centroids and edges’ middle points of elements having common nodes. The proposed elements, namely NS-MITC3, show good accuracy and convergence as compared to other plate elements when employed to analyze laminated composite plates.