An upper-bound limit analysis of Mindlin plates using CS-DSG3 method and second-order cone programming

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

“…For more details of the formulation of the CS-DSG3, the interested readers are encouraged to refer to the literature. 51–60…”

“…The CS-DSG3, 46 a numerical method belonging to the group of the smoothed finite element methods, 50 was proposed for dealing with the mechanical analysis of the plate-like structures. In recent years, this method has been applied successfully for various structures such as isotropic plates, isotropic shells and composite plates [51][52][53][54][55][56][57][58][59][60] etc. In this paper, the CS-DSG3 will be extended for free vibration analysis of laminated FG-CNTRC quadrilateral plates and the brief formulation of the CS-DSG3 is presented as given below.…”

“…For more details of the formulation of the CS-DSG3, the interested readers are encouraged to refer to the literature. [51][52][53][54][55][56][57][58][59][60] In the present CS-DSG3, the domain discretization is the same as that of the discrete shear gap (DSG3) method 61 using N n nodes and N e triangular elements. However, in the formulation of the CS-DSG3, each triangular element e is further divided into three sub-triangles Á 1 , Á 2 and Á 3 by connecting the central point O of the element to three field nodes as shown in Figure 2.…”

Static and free vibration analyses of stiffened folded plates using a cell-based smoothed discrete shear gap method (CS-FEM-DSG3)

“…The numerical results indicated that the CS-FEM-DSG3 is free of shear locking and achieves high accuracy compared to the exact solutions and other existing elements in the literature. Due to these outstanding properties, the CS-FEM-DSG3 then has been extended to analyze various kinds of structures such as flat shells [45], bare and stiffened isotropic Mindlin plates [46][47][48], cracked Mindlin plate [49], FGM plates [50], composite plates [51,52] and piezoelectricity plates [53]. An overview related to the recent development of the CS-FEM-DSG3 can be found in Ref.…”

Static Limit Analysis of Reinforced Soil Structures by a Simple Finite Element and Second-Order Cone Programming

“…Under certain restrictions, the theory of plasticity allows the prediction of the collapse load by means of the limit analysis based on the bound theorems (Drucker et al, 1952 União,in this case coupling such theorems with the finite element method, as originally proposed by Lysmer (1970) and Bottero et al (1980). This is a straightforward approach for computing lower and upper bounds on the load at incipient collapse which have gained increasing attention (Lyamin and Sloan, 2002;Krabbenhoft and Damkilde, 2003;Makrodimopoulos and Martin, 2006;Yu and Tin-Loi, 2006;Ciria et al, 2008;Munõz et al, 2009;Le et al, 2010;Bleyer and de Buhan, 2014;Nguyen-Thoi et al, 2015). This is partly due to the development of robust optimization methods and solvers on which they strongly rely (Drud, 1996;Sturm, 1999;Lyamin and Sloan, 2002;Murtagh and Saunders, 2003;Tütüncü et al, 2003;Andersen et al, 2003;Krabbenhoft and Damkilde, 2003).…”