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The problem of the buckling of finite length externally constrained thin circular cylinders is solved to yield a generalized eigenvalue problem with constraint conditions. The solution is based on an inverse iteration procedure in which the non-linear complementary equation is solved by a non-smooth version of Newton's method that saves computer time and space when compared to a linear complementary algorithm. The numerical results show that the method proposed is effective and that the critical buckling load of the constrained cylinder is almost independent of the length of the cylinder, unlike the critical load of free (unconstrained) thin cylinders. In the direction of its axis, the shell is discretized by finite strips which circumferentially use straight bar and beam displacement functions. It is proved that when the widths of the strips approach zero, the geometrical relationships used in this paper approach those of Koiter–Sanders cylindrical shell theory. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A generalized finite element for buckling analysis of tapered columns with various cross sections is established by using Chebyshev polynomial approach to the governing differential equation in this paper. The proposed formulation involves the effects of shear deformation and is therefore applicable to lattice columns. The change of the sectional properties along the length direction can be calculated exactly in the FE analysis. Buckling of a tapered lattice column, with respective lace bars and batten plates, is studied in the numerical example. The effects of shear deformation on the buckling loads of tapered lattice columns are specified. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The lateral buckling of a simply supported symmetric thin-walled member is investigated. An energy equation for the lateral buckling of thin-walled member has been presented in which the effects of torsion and assumed warping are taken into account. Using variation method helps to derive the governing differential equation together with appropriated boundary conditions. The lateral buckling loads are obtained by solving the differential equation numerically using Galerkin's method of weighted residuals. The method presented in this paper yields the formula for computing the lateral buckling load that is very simple and straightforward. By the study, a very complex practical eigenvalue problem can be transformed into a very simple one. The results predicted with the analytical method are in good agreement with the ones obtained by experimental, finite integral, non-linear finite element methods and optimal analysis. The fast convergence of the method makes it possible to write the resulting formulae in a likely closed form which is very simple and very convenient to use. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a one-dimensional finite element for creep buckling analysis of structures comprised of straight and prismatic beam members. Spatial displacements and rotations are allowed to be large while strains are assumed to be small. Material is assumed to be homogenous and isotropic. The corresponding equilibrium equations are formulated in the framework of co-rotational description, using the virtual work principle. In contrast to conventional co-rotational formulation, which is linear on element level and unable to model Wagner effect, in this paper an additional nonlinear part of stiffness matrix is evaluated and added to standard elastic stiffness. Implementation of developed numerical algorithm is demonstrated through few test problems. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A method of identifying the critical load of structures, the buckling shape of which is constrained, is presented based on two novel techniques. The first identifies this critical or limit point buckling value using a linear, complementary algorithm to solve what is shown to be a quadratic programming problem, while the second adopts a generalized inverse iteration technique. The critical load of a circular ring confined by a rigid circular boundary and subject to thermal expansion is then obtained using this technique, and it is found that it is lower than that previously obtained from a traditional approach based on energy considerations. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Second-order post-buckling fields emanate from the solutions of a constrained minimization problem. Two iterative solution algorithms for this specific type of constrained problem are described. A classical augmented Lagrangian algorithm is compared with a simpler one utilizing the specific feature of the initial post-buckling analysis. Numerical examples of prismatic plate-type structures are presented. [ABSTRACT FROM AUTHOR]

In this paper, the problem for evaluating the eigenvalues in the buckling problem and the natural vibration problem of the bending bar is reduced to finding zeros of a function, which is called the target function T(ω) in this paper. The explicit forms of the target functions can be obtained for all possible boundary value problems. The functions depend on the numerical solution of the fundamental problems. The zeros of the target functions will be the required eigenvalues. Finally, several numerical examples are given to demonstrate the use of the suggested method. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The investigation of the non-linear response of shell-like structures requires insight into stability behavior. In the paper we compare two strategies to compute singular points based on different eigenvalue problems. We show a simple algorithm to calculate critical load factors A used in engineering buckling analysis from the eigenvalues of the standard eigenvalue problem (KT - ωl)φ = 0. Some numerical examples illustrate the derived results and algorithms. [ABSTRACT FROM AUTHOR]

The generic equilibrium equations of arbitrarily loaded pre-stressed non-prismatic shear deformable composite beams can be derived. The buckling equilibrium equations can be obtained by simplifying the generic equilibrium equations. These equations can be used to develop the differential quadrature element method (DQEM) analysis model of the buckling of shear deformable beams. The DQEM uses the DQ to discretize the buckling equilibrium equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results of the buckling of shear deformable bar structures solved by the developed numerical algorithm are presented. They prove that the DQEM buckling analysis model is efficient in comparison of convergence rate and numerical stability with the existing numerical techniques such as traditional FDM and some FEM models. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present study concerns the dynamic behaviour of a space arc subject to a midarc vertical buckling load dynamically applied. The arc is discretized with a set of three-dimensional beam finite elements and the non-linear dynamic equation (large displacements) is solved by means of an unconditionally stable time-dependent scheme over time. The vertical excitation gives rise to a very fast and erratic horizontal wave as the structure begins to vibrate in all directions. This horizontal wave has chaotic characteristics as its attractor indicates. Time–displacement curves are obtained for all components of the midarc point. Although the time algorithm was executed here for 2000 time steps, simulation over longer periods of time can reveal the vibration characteristics and even simulate structural failure under the imposed dynamic buckling load for the space arc structure. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present study proposes an innovated eigenanalysis-free idea to extract the buckling mode only from the LDLT-decomposed stiffness matrix in large-scale bifurcation analysis. The computational cost for extracting the critical eigenvector is negligible, because the decomposition of the stiffness matrix will continually be repeated during path-tracing to solve the stiffness equations. A numerical example is computed to illustrate that the proposed idea is tough enough even for multiple bifurcation. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop a general method, called the spline finite member element method, for predicting the effect of shearing strains in the middle surface of the walls on the buckling of thin-walled members with any cross-section because the classical theory of thin-walled members is based on the assumption of no shearing strains and is unable to reflect the shear lag phenomenon. A governing energy equation for the buckling has been derived in which the effects of torsion, warping of the member and, especially, the shearing strains in the middle surface of the wall are taken into account. The accuracy of the method is tested based on some available closed-form solutions. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new discrete singular convolution (DSC) method is developed for vibration, buckling and static analyses of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for straight-sided quadrilateral thin plates such as rectangular, skew, trapezoidal and rhombic plates are presented. The results obtained by the DSC method were compared with those obtained by the other numerical and analytical methods. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We address here some computational aspects of the natural-mode finite element method (NM-FEM), a technique recently developed by the authors for the analysis of arbitrary composite shells. We consider in particular a model problem comprising a (45/-45/0/90)S cylindrical composite shell with 2398 degrees of freedom subjected to compressive load and temperature increase, and compute the first four critical loads and temperatures. For this problem a computational statistics report is obtained showing the breakdown of the CPU time in the various routines. It is observed that most of the computing time is spent on algebraic operations, suggesting computational efficiency and high potential for vectorization/parallelization. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A new method for computation of buckling load and mode shape of a non-uniform column is proposed. Based on the principles of calculus of variations the stability analysis of the column is defined as an optimization problem. Different known techniques of optimization are candidates for solution process. Through analysis of typical columns and comparison of the results with those of other methods, the basic theory and implementation of the presented method is verified. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An algorithm combining the numerical execution in time of implicit and explicit methods of solution is presented in this paper. The algorithm swaps between both methods as required for the analysis. The whole mesh is solved for an unique method at once, i.e. there are no partitions of the mesh for separate implicit or explicit treatment of the solution. The combination is in-time, in such a manner that if the implicit method starts diverging the explicit one is initiated by appropriate conditions of transition. The formulation is presented first and its implementation is validated by the analysis of a key numerical example. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper new forms are introduced for efficient eigensolution of special tri-diagonal and five-diagonal matrices. Applications of these forms are illustrated using problems from mechanics of structures. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Some physical problems require finding roots of branching functions. Transcendental eigenvalue problems are a common example, where certain functions are known to be branching, monotonic within branches, and have root counting algorithms. Solution conventionally starts by surrounding a required root with bounds on the same branch, and then refining one or both of the estimates by conventional or problem-specific algorithms. Here, difficulties caused by branching are removed by defining a new function that is free of branches and has a single root. The root of this function is found by linear interpolation, with some acceleration applied if high accuracy is wanted. Construction of the new function is completely numerical, as is the root finding acceleration. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The present study is concerned with the dynamic collapse of cantilever isotropic and composite cylinders. The cylinders are initially subjected to critical compressive loads at the free edge. A small increase in these critical loads is then dynamically applied in the form of a sinusoidal excitation using the first natural frequency of the system. The results show that there exists a small time period whereby small dynamic excitations take place. Following this short time period, sudden large dynamic displacements occur which cause the collapse of the structure. This phenomenon takes place very near to the buckling load. An implicit unconditionally stable time scheme is applied to trace the dynamic behaviour of the structure. The effect of the excitation frequency on the response is also assessed. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a new iterative method based on Padé approximants for numerical analysis of non-linear problems. It improves on the classical iterative Newton methods. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper highlights the results of numerical experimentation with a geometrically non-linear formulation of a thick axisymmetric shell element involving non-axisymmetric deformation. The formulation itself has earlier been presented in the context of a non-linear local–global analysis of shells of revolution, where very little attention was paid to an independent evaluation of the element's performance. A Fourier decomposition of the loads and the displacements has been used in the circumferential co-ordinate, in order to describe the non-axisymmetric behavior. Due to the interaction between different harmonic terms in the non-linear analysis, the tangential stiffness matrix is no longer block-diagonal. A pseudoload method and a conjugate gradient like iterative scheme have been used to overcome the problem of a large tangent stiffness matrix, and thus most of the advantages of the semi-analytical method have been retained in the non-linear analysis. The accuracy of the predictions in the study has been benchmarked by analysing the same examples using the quadrilateral shear deformable shell element available in the commercial code NISA II. A comparison with other results available in the literature hints that the effect of transverse shear deformation should not be neglected in the geometrically non-linear analysis of shells which are traditionally considered thin. © 1997 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A three-dimensional finite element model is proposed for the fiber interaction effects during fiber microbuckling in fiber-reinforced composites. The model considers an elastic matrix reinforced by a periodic fiber series subjected to compression in axial direction. It accounts for the distinct difference in mechanical properties of the reinforcement and the matrix, as well as for the spatial problem character at the fiber–matrix scale. Perfect bonding at the fiber–matrix interfaces and the periodicity of the buckled system in the plane of fibers (in-plane microbuckling) are assumed. For comparison purposes, a dilute approximation model dealing with a single fiber in a matrix is presented as well. An eigenvalue analysis of the considered systems fiber–matrix is performed. Calculations are carried out for the cases of both isotropic and transversal isotropic fibers in elastic isotropic matrices. Results show that the fiber interaction results in a significant increase in the buckling wavelength and in an important decrease in the critical shortening. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The authors have already proposed in their previous papers an innovative eigenanalysis-free idea to extract the buckling mode for bifurcation instability from the LDLT-decomposed stiffness matrix. The present study first outlines this basic idea very briefly for a review purpose. The idea will then be applied to eigenvector-free procedures for identifying and pinpointing the stability point and branch-switching for post-bifurcation analysis. Numerical examples will examine the versatility and robustness of the proposed eigenvector-free procedures in computational bifurcation theory. It is illustrated that the proposed procedures are robust enough for multiple as well as simple bifurcation. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An updated Lagrangian formulation of the generalized conforming flat shell element with drilling degrees of freedom is derived based on the incremental equation of virtual work of a three-dimensional (3D) continuum for a purely geometric non-linear analysis of the space structure. While solving the non-linear equations, the Euler–Newton method and modified Euler–Newton method are used in static analyses, and the modified arc-length method and Newton arc-length method for post-buckling problems. A number of numerical examples are given to demonstrate the effectiveness of the proposed approach and programs. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates numerically and experimentally the influence of initial geometric imperfections on the critical loads of initially stretched thick hyperelastic cylindrical shells under increasing uniform internal pressure. Imperfections in shells can have a global or local character. First, two types of local imperfections are considered: (1) a local axially symmetric imperfection in the form of a ring and (2) a small rectangular imperfection. The influence of the imperfection thickness, position and size are analysed in detail. Results show that the critical load decreases as the imperfections increase in size or thickness and as they move from the boundaries to the centre of the shell. The influence of multiple local imperfections is also studied in the present paper. Finally, the influence of global imperfections is considered with the imperfections described as a variation of the shell curvature in the axial direction. The results show that thick hyperelastic shells may be sensitive to local and global imperfections. In all cases the experimental results are in good agreement with the numerical ones, corroborating the conclusions. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]