774 research outputs found
A cell-based smoothed finite element method for kinematic limit analysis
This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged
Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements
In this article, we combine Carrera’s Unified Formulation (CUF) [13] and [7] and cell based smoothed finite element method [28] for studying the static bending and the free vibration of thin and thick laminated plates. A 4-noded quadrilateral element based on the field consistency requirement is used for this study to suppress the shear locking phenomenon. The combination of cell based smoothed finite element method and field consistent approach with CUF allows a very accurate prediction of field variables. The accuracy and efficiency of the proposed approach are demonstrated through numerical experiments
Analysis of composite plates through cell-based smoothed finite element and 4-noded mixed interpolation of tensorial components techniques
The static bending and the free vibration analysis of composite plates are performed with Carrera's Unified Formulation (CUF). We combine the cell-based smoothed finite element method (CSFEM) and the 4-noded mixed interpolation of tensorial components approach (MITC4). The smoothing method is used for the approximation of the bending strains, whilst the mixed interpolation allows the calculation of the shear transverse stress in a different manner. With a few numerical examples, the accuracy and the efficiency of the approach is demonstrated. The insensitiveness to shear locking is also demonstrated. © 2014 Elsevier Ltd. All rights reserved
Analysis and control of geometrically nonlinear responses of piezoelectric FG porous plates with graphene platelets reinforcement using B\'ezier extraction
In this study, we propose an effective numerical approach to analyse and
control geometrically nonlinear responses for the functionally graded (FG)
porous plates reinforced by graphene platelets (GPLs) integrated with
piezoelectric layers. The basis idea is to use isogeometric analysis (IGA)
based on the B\'ezier extraction and the -type higher-order shear
deformation theory (-HSDT). By applying the B\'ezier extraction, the
original Non-Uniform Rational B-Spline (NURBS) control meshes can be
transformed into the B\'ezier elements which allow us to inherit the standard
numerical procedure like the finite element method (FEM). The mechanical
displacement field is approximated based on the -HSDT whilst the electric
potential is assumed to be a linear function through the thickness of each
piezoelectric sublayer. The FG plate contains the internal pores and GPLs
dispersed in the metal matrix either uniformly or non-uniformly according to
various different patterns along the thickness of plate. In addition, to
control dynamic responses, two piezoelectric layers are perfectly bonded on the
top and bottom surfaces of the FG plate. The geometrically nonlinear equations
are solved by the Newton-Raphson iterative procedure and the Newmark's time
integration scheme. The influences of the porosity coefficients, weight
fractions of GPLs as well as the external electrical voltage on the
geometrically nonlinear behaviours of the plates with different porosity
distributions and GPL dispersion patterns are evidently investigated through
numerical examples. Then, a constant displacement and velocity feedback control
approaches are adopted to active control the geometrically nonlinear static as
well as the dynamic responses of the FG porous plates, where the effect of the
structural damping is considered, based on a closed-loop control with
piezoelectric sensors and actuators.Comment: 39 pages, 20 figure
Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates
In this study, an efficient polygonal finite element method (PFEM) in combination with quadratic serendipity shape functions is proposed to study nonlinear static and dynamic responses of functionally graded (FG) plates with porosities. Two different porosity types including even and uneven distributions through the plate thickness are considered. The quadratic serendipity shape functions over arbitrary polygonal elements including triangular and quadrilateral ones, which are constructed based on a pairwise product of linear shape functions, are employed to interpolate the bending strains. Meanwhile, the shear strains are defined according to the Wachspress coordinates. By using the Timoshenko's beam to interpolate the assumption of the strain field along the edges of polygonal element, the shear locking phenomenon can be naturally eliminated. Furthermore, the C0–type higher-order shear deformation theory (C0–HSDT), in which two additional variables are included in the displacement field, significantly improves the accuracy of numerical results. The nonlinear equations of static and dynamic problems are solved by Newton–Raphson iterative procedure and by Newmark's integration scheme in association with the Picard methods, respectively. Through various numerical examples in which complex geometries and different boundary conditions are involved, the proposed approach yields more stable and accurate results than those generated using other existing approaches
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