1,720,981 research outputs found
MITC9 shell elements based on refined theories for the analysis of isotropic cylindrical structures.
Full text linkIn this work a nine-nodes shell finite element, formulated in the framework of Carrera’s Unified Formulation (CUF), is presented. The exact geometry of cylindrical shells is considered. The Mixed Interpolation of Tensorial Components (MITC) technique is applied to the element in order to overcome shear and membrane locking phenomenon. High-order equivalent single layer theories contained in the CUF are used to perform the analysis of shell structures. Benchmark solutions from the open literature are taken to validate the obtained results. The mixed-interpolated shell finite element shows good properties of convergence and robustness by increasing the number of used elements and the order of expansion of displacements in the thickness direction
Refined shell finite elements based on RMVT and MITC for the analysis of laminated structures
No full textIn this paper, we present some advanced shell models for the analysis of multilayered structures in which the mechanical and physical properties may change in the thickness direction. The finite element method showed successful performances to approximate the solutions of the advanced structures. In this regard, two variational formulations are available to reach the stiffness matrices, the Principle of Virtual Displacement (PVD) and the Reissner Mixed Variational Theorem (RMVT). Here we introduce a strategy similar to MITC (Mixed Interpolated of Tensorial Components) approach, in the RMVT formulation, in order to construct an advanced locking-free finite element. Moreover, assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. We show that in the RMVT context, the element exhibits both properties of convergence and robustness when comparing the numerical results with benchmark solutions from literature. © 2014 Elsevier Ltd
Refined multilayered shell elements based on MITC type technique and Unified Formulation
Full text linkApproximation of functionally graded plates with non-conforming finite elements
No full textAbstractIn this paper rectangular plates made of functionally graded materials (FGMs) are studied. A two-constituent material distribution through the thickness is considered, varying with a simple power rule of mixture. The equations governing the FGM plates are determined using a variational formulation arising from the Reissner–Mindlin theory. To approximate the problem a simple locking-free Discontinuous Galerkin finite element of non-conforming type is used, choosing a piecewise linear non-conforming approximation for both rotations and transversal displacement. Several numerical simulations are carried out in order to show the capability of the proposed element to capture the properties of plates of various gradings, subjected to thermo-mechanical loads
Approximation of anisotropic multilayered plates through RMVT and MITC elements
No full textThis paper presents a mixed two dimensional model for the analysis of mechanical response in anisotropic multilayered plates, with particular attention to the behavior along the thickness of the plate. It is well known that the study of anisotropic material structures requires to take into account cross-elasticity effects that make the solution converge very slowly. The finite element method showed successful performances to approximate the solutions of these structures. In this regard, two variational formulations are available to calculate the stiffness matrix, the Principle of Virtual Displacement (PVD) and the Reissner Mixed Variational Theorem (RMVT). Here, a strategy similar to MITC (Mixed Interpolated of Tensorial Components) approach, in the RMVT formulation, is adopted to formulate advanced locking-free finite elements. Then, assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. The displacement field is defined according to the Reissner–Mindlin theory and the shear stresses are assumed parabolic along the thickness by means of RMVT. The normal strain ∊zz and the normal stress σzz are discarded. The shear stresses σxz and σyz are interpolated in each element according to the MITC. By comparing the results with benchmark solutions from literature, it is shown that the element exhibits both properties of convergence and robustness and provides very accurate results in terms of transverse shear stresses of the anisotropic multilayered plate
Reissner's Mixed Variational Theorem toward MITC finite elements for multilayered plates
Full text linkIn this paper, we analyze a two dimensional model of multilayered plates for which the main interest is to study the mechanical and physical properties, that may change in the thickness direction. The finite element method showed successful performances to approximate the solutions of the advanced structures. In this regard, two variational formulations are available to reach the stiffness matrices, the principle of virtual displacement (PVD) and the Reissner mixed variational theorem (RMVT). Here we introduce a strategy similar to Mixed Interpolated of Tensorial Components (MITC) approach, in the RMVT formulation, in order to construct an advanced locking-free finite element. Assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. It is known that unless the combination of finite element spaces for displacement and stresses is chosen carefully, the problem of locking is likely to occur. Following this suggestion, we propose a finite element scheme that it is known to be robust with respect to the locking phenomenon in the classical PVD approach. We show that in the RMVT context, the element exhibits both properties of convergence and robustness when comparing the numerical results with benchmark solutions from literature. © 2012 Elsevier Ltd
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