In this paper, three-dimensional elastic deformation of isotropic functionally graded plates subj... more In this paper, three-dimensional elastic deformation of isotropic functionally graded plates subjected to point loading is investigated using a combination of analytical and computational means. The analytical approach is based on the displacement functions method, while numerical modeling, which requires high accuracy in the representation of the point loading, uses Galerkin type finite element method. Three different plate geometries are examined for validation purposes, and the difficulties associated with an optimum choice of the element size are discussed. It is shown that by using a posteriori error estimation based on the equivalent stress measure accurate results can be obtained even in the neighborhood of the point loading.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
An analytical model founded on geometric and potential energy principles for kink band deformatio... more An analytical model founded on geometric and potential energy principles for kink band deformation in laminated composite struts is presented. It is adapted from an earlier successful study on confined layered structures that was formulated to model kink band formation in the folding of geological layers. This study's principal aim was to explore the underlying mechanisms governing the kinking response of flat, laminated components comprising unidirectional composite laminae. A pilot parametric study indicates that the key features of the mechanical response are captured well and that quantitative comparisons with experiments presented in the literature are highly encouraging.
IMA Journal of Applied Mathematics (2011) 76, 120−145 doi:10.1093/imamat/hxq062 Advance Access pu... more IMA Journal of Applied Mathematics (2011) 76, 120−145 doi:10.1093/imamat/hxq062 Advance Access publication on December 16, 2010 ... Semi-analytical modelling of buckling driven delamination in uniaxially compressed damaged plates ... M. AHMER WADEE∗ AND CHRISTINA V¨ ...
An approach of numerical modeling of heterogeneous, functionally graded materials, by using the f... more An approach of numerical modeling of heterogeneous, functionally graded materials, by using the finite element method, is proposed. The variational formulation is derived from the generic case so that the implementation of material coefficients, which are functions in space, is realized without any further assumptions. An analytical solution for a simple case is presented and used for validation of the numerical model.
A geometrically nonlinear model is developed to investigate the buckling behaviour of plates with... more A geometrically nonlinear model is developed to investigate the buckling behaviour of plates with a pre-existing delamination under uniaxial compression. The Rayleigh–Ritz procedure, based on trigonometric out-of-plane displacement functions, is used in conjunction with potential energy principles to describe the buckling and postbuckling response. The formulation is enhanced with the introduction of a discrete cohesive zone model to allow the delamination to grow under further loading. Different cases are investigated with residual capacities of the plates being evaluated in the neighbourhood of a transitional depth of delamination, where the postbuckling behaviour changes from thin film to mixed mode to global buckling. The model is validated with the commercial finite-element code Abaqus and criteria are proposed such that the component may be exploited beyond the critical loads.
A geometrically nonlinear plate model has been developed analytically in order to investigate the... more A geometrically nonlinear plate model has been developed analytically in order to investigate the buckling behaviour of laminated composite panels containing a centrally located delaminated patch. The panels examined are rectangular and under uniaxial compression. ...
Philosophical Transactions of the Royal Society A, Mar 19, 2012
An analytical model founded on geometric and potential energy principles for kink band deformatio... more An analytical model founded on geometric and potential energy principles for kink band deformation in laminated composite struts is presented. It is adapted from an earlier successful study on confined layered structures that was formulated to model kink band formation in the folding of geological layers. This study's principal aim was to explore the underlying mechanisms governing the kinking response of flat, laminated components comprising unidirectional composite laminae. A pilot parametric study indicates that the key features of the mechanical response are captured well and that quantitative comparisons with experiments presented in the literature are highly encouraging.
In this paper, three-dimensional elastic deformation of isotropic functionally graded plates subj... more In this paper, three-dimensional elastic deformation of isotropic functionally graded plates subjected to point loading is investigated using a combination of analytical and computational means. The analytical approach is based on the displacement functions method, while numerical modeling, which requires high accuracy in the representation of the point loading, uses Galerkin type finite element method. Three different plate geometries are examined for validation purposes, and the difficulties associated with an optimum choice of the element size are discussed. It is shown that by using a posteriori error estimation based on the equivalent stress measure accurate results can be obtained even in the neighborhood of the point loading.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
An analytical model founded on geometric and potential energy principles for kink band deformatio... more An analytical model founded on geometric and potential energy principles for kink band deformation in laminated composite struts is presented. It is adapted from an earlier successful study on confined layered structures that was formulated to model kink band formation in the folding of geological layers. This study's principal aim was to explore the underlying mechanisms governing the kinking response of flat, laminated components comprising unidirectional composite laminae. A pilot parametric study indicates that the key features of the mechanical response are captured well and that quantitative comparisons with experiments presented in the literature are highly encouraging.
IMA Journal of Applied Mathematics (2011) 76, 120−145 doi:10.1093/imamat/hxq062 Advance Access pu... more IMA Journal of Applied Mathematics (2011) 76, 120−145 doi:10.1093/imamat/hxq062 Advance Access publication on December 16, 2010 ... Semi-analytical modelling of buckling driven delamination in uniaxially compressed damaged plates ... M. AHMER WADEE∗ AND CHRISTINA V¨ ...
An approach of numerical modeling of heterogeneous, functionally graded materials, by using the f... more An approach of numerical modeling of heterogeneous, functionally graded materials, by using the finite element method, is proposed. The variational formulation is derived from the generic case so that the implementation of material coefficients, which are functions in space, is realized without any further assumptions. An analytical solution for a simple case is presented and used for validation of the numerical model.
A geometrically nonlinear model is developed to investigate the buckling behaviour of plates with... more A geometrically nonlinear model is developed to investigate the buckling behaviour of plates with a pre-existing delamination under uniaxial compression. The Rayleigh–Ritz procedure, based on trigonometric out-of-plane displacement functions, is used in conjunction with potential energy principles to describe the buckling and postbuckling response. The formulation is enhanced with the introduction of a discrete cohesive zone model to allow the delamination to grow under further loading. Different cases are investigated with residual capacities of the plates being evaluated in the neighbourhood of a transitional depth of delamination, where the postbuckling behaviour changes from thin film to mixed mode to global buckling. The model is validated with the commercial finite-element code Abaqus and criteria are proposed such that the component may be exploited beyond the critical loads.
A geometrically nonlinear plate model has been developed analytically in order to investigate the... more A geometrically nonlinear plate model has been developed analytically in order to investigate the buckling behaviour of laminated composite panels containing a centrally located delaminated patch. The panels examined are rectangular and under uniaxial compression. ...
Philosophical Transactions of the Royal Society A, Mar 19, 2012
An analytical model founded on geometric and potential energy principles for kink band deformatio... more An analytical model founded on geometric and potential energy principles for kink band deformation in laminated composite struts is presented. It is adapted from an earlier successful study on confined layered structures that was formulated to model kink band formation in the folding of geological layers. This study's principal aim was to explore the underlying mechanisms governing the kinking response of flat, laminated components comprising unidirectional composite laminae. A pilot parametric study indicates that the key features of the mechanical response are captured well and that quantitative comparisons with experiments presented in the literature are highly encouraging.
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Papers by C. Vollmecke