Isoparametric Spline Finite Strip Research Articles

Elastic and inelastic buckling of square and skew FGM plates with cutout resting on elastic foundation using isoparametric spline finite strip method

The elastic buckling of square and skew thin functionally graded material (FGM) plates with cutout resting on an elastic foundation is investigated using the isoparametric spline finite strip method. It is assumed that the material properties of FGM plates vary smoothly through the thickness according to the power law model. The elastic foundation is simulated by the Winkler and two-parameter Pasternak models. The isoparametric spline finite strip method is also applied to investigate initial inelastic local buckling loads of skew homogenous plates with cutout based on the Ramberg–Osgood representation of the stress–strain curve using the deformation theory of plasticity. The critical buckling load of the plate is achieved by minimizing its total potential energy and solving the corresponding eigenvalue problem. In addition, the effects of elastic foundation coefficients and hole size on the local buckling of plates with different boundary conditions are determined and discussed.

Inelastic local buckling behaviour of perforated plates and sections under compression

A recently developed inelastic large displacement isoparametric spline finite strip method was used to investigate the inelastic stress distributions, load transfers and failure modes for a range of hole shapes, sizes and spacings. While such study is available for elastic material behaviour, the influence of yielding on the load transfers in and failure modes of perforated plates and sections is not well understood. This study considers perforated simply supported plates under compression and perforated C-section columns in compression failing by local buckling. Several inelastic material models were included in the study, including elastic perfectly-plastic and linear hardening models, and a model with nonlinear yielding and isotropic hardening. Comparisons are made with elastic analyses and conclusions are drawn about the influence of yielding and strain hardening on the stress distributions, load transfers and failure modes of typical thin-walled metallic plates and structural sections.

Inelastic initial local buckling of skew thin thickness-tapered plates with and without intermediate supports using the isoparametric spline finite strip method

In this paper, skew isotropic plates subjected to in-plane loadings are analyzed using a stability analysis based on the isoparametric spline finite strip method, which includes inelasticity. Using this method, the initial inelastic local buckling of skew plates with or without intermediate line supports is studied based on Ramberg–Osgood representation of the stress–strain curve using the deformation theory of plasticity. Stiffness and stability matrices are formulated by energy expressions using the small deflection theory. The effect of tapered section on the local buckling of skew plates is taken into account. Finally, the inelastic local buckling loads of these plates are obtained and the results are compared with known solutions in the literature.

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Analytical developments

This paper presents the analytical developments of the application of the Isoparametric Spline Finite Strip Method (ISFSM) to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics, strain–displacement and constitutive assumptions are presented, and the tangential stiffness matrix is derived by applying the incremental equilibrium condition. The requirements for strip continuity and boundary conditions are also discussed. In particular, the plasticity theory and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The present isoparametric spline finite strip analysis is verified against a number of analyses of perforated and non-perforated plates and plate assemblages, as described in the companion paper (Yao and Rasmussen, submitted for publication) [1], demonstrating its accuracy and efficiency for the predictions of the inelastic post-buckling behavior of perforated thin-walled steel structures.

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Numerical investigations

The theoretical developments of a material inelastic and geometric nonlinear analysis by use of the isoparametric spline finite strip method (ISFSM) are presented in a companion paper (Yao and Rasmussen (submitted) [1]). In the present paper, the numerical implementation of the analysis is reported, including nonlinear solution techniques, inelastic material models, selective reduced integration strategies, convergence criteria, and solution procedures. The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.

Geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled structures

This paper presents the application of the isoparametric spline finite strip method to the geometric nonlinear analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics, strain–displacements and constitutive assumptions are described and applied to the spline finite strip method. The derivation of the tangential and secant stiffness matrices is presented by applying the equilibrium condition and its incremental form. The reliability of the method is demonstrated by applying the method to classical nonlinear complex plate and shell problems as well as the geometric nonlinear analysis of perforated flat and stiffened plates.

Linear elastic isoparametric spline finite strip analysis of perforated thin-walled structures

This paper describes the application of the isoparametric spline finite strip method to the linear elastic analysis of tri-dimensional perforated folded plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics assumptions and the procedure for combining in-plane (membrane) and bending effects are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square stiffened perforated plates in compression and bending are analysed.

Isoparametric spline finite strip method for the bending of perforated plates

AbstractThe isoparametric spline finite strip method was recently applied by the authors to the linear elastic in‐plane stress analysis of perforated thin‐walled structures. In this paper, the application of the method is extended to the bending of perforated plates. The paper describes the theory of the isoparametric spline finite strip method in the context of Mindlin plate bending theory. It sets out the strain–displacement and stress–strain relationships and derives expressions for the local and global stiffness matrices. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square plates in bending containing openings of different shapes are analysed. Copyright © 2007 John Wiley & Sons, Ltd.

Elastic buckling analysis of perforated thin-walled structures by the isoparametric spline finite strip method

This paper presents the application of the isoparametric spline finite strip method to the elastic buckling analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. The kinematics assumptions, strain–displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.

Static and free vibration analysis of variable-depth bridges of arbitrary alignments using the isoparametric spline finite strip method

The isoparametric spline finite strips for shells are employed to solve static and free vibration problems of variable-depth bridges of arbitrary alignments. Using this approach, a continuous bridge is first split up into substructures. Each substructure is modelled as an assemblage of isoparametric spline finite strips. Compatibility between substructures is ensured by suitable transformation at the interface. The presence of support diaphragms and bearings can also be accounted for. This method retains the computational efficiency of the spline finite strip method while it is much more flexible in geometric modelling. Solutions of this method are compared with other available solutions, and good agreement is observed.

Free vibration and stability analysis of shells by the isoparametric spline finite strip method

The isoparametric spline finite strip method has been applied to the free vibration and stability analysis of shells. The convergence of the method is reviewed critically. Additional numerical examples on shells of different geometry are also employed to demonstrate the efficiency, accuracy and versatility of the method.

Isoparametric spline finite strip for degenerate shells

The isoparametric spline finite strip method for degenerate shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. In this paper, the general theory of isoparametric spline finite strip for analysis of shell structures is outlined. The method, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort. Solutions of a number of problems using this method are compared with other available analytical and numerical solutions, and in all cases very good agreement is observed.

Isoparametric spline finite strip for plane structures

The isoparametric spline finite strip methods for Mindlin plate bending, plane stress and plane strain problems are presented. The essence of the method lies in the use of uniform cubic B- spline curves in the modelling of the geometry and representation of the displacement field. In this paper, the general theory of isoparametric spline finite strip for analysis of plane structures is outlined. The method, when applied to most problems, yields a relatively narrow band matrix and requires little computational effort. Solutions of this method are compared with other available experimental, analytical and numerical solutions, and in all cases very good agreement is observed.