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1 – 10 of over 4000Krzysztof Wiśniewski and Robert L. Taylor
Numerical aspects of initial stability analysis of a cylindrical shell of non‐constant parameters along the generator and under non‐symmetrical loads are considered. A variational…
Abstract
Numerical aspects of initial stability analysis of a cylindrical shell of non‐constant parameters along the generator and under non‐symmetrical loads are considered. A variational approach based on Sanders' and Donnell's non‐linear equations of thin, elastic shells is applied. The problem is decomposed to determine: the stability vectors in the axial direction in the first step, and the critical load and the stability vector in the circumferential direction in the second step. The discretization is based on finite Fourier representations and the finite difference method. To find the approximate stability vector in the axial direction an auxiliary problem for axisymmetric loads is solved. The error of the method is defined and the effectiveness of the method is estimated. The decomposition leads to small and fast algorithms suitable for personal computers. Shells with constant and stepped thicknesses under wind loads are calculated as examples. Tested algorithms show considerable effectiveness and good accuracy of results.
Bahram Nour‐Omid and Robert L. Taylor
A data structure is described that stores only the non‐zero terms of the assembled stiffness matrix. This storage scheme results in considerable reduction in memory demand during…
Abstract
A data structure is described that stores only the non‐zero terms of the assembled stiffness matrix. This storage scheme results in considerable reduction in memory demand during the assembly phase of a finite element program. Therefore, larger matrices can be formed in the main memory of the computer. When secondary store must be used this approach reduces the I/O cost during the assembly stage. An algorithm is derived that starts with the element connectivity information and generates the compacted data structure. The element matrices are then assembled to form the stiffness matrix with this storage scheme. The assembly algorithm is described and a FORTRAN listing of the routines is presented. The reduction in storage is demonstrated with the aid of numerical examples.
Harn C. Chen and Robert L. Taylor
The Lanczos vectors and the Ritz vectors have been used for computing the dynamic response of linear structures. Although the procedures of using these two sets of vectors appear…
Abstract
The Lanczos vectors and the Ritz vectors have been used for computing the dynamic response of linear structures. Although the procedures of using these two sets of vectors appear similar to the procedure of using the eigenvectors to find an approximate solution, the fundamental mechanisms of the three are different. We compare the three sets of vectors in detail to show some of the important differences in the hope that this comparison will be helpful to the use of the Lanczos vectors or the Ritz vectors for computing dynamic responses.
Panayiotis Papadopoulos and Robert L. Taylor
This paper addresses the loading/unloading conditions of thediscrete initial—value problem of plastic flow at infinitesimal deformations. As in the continuum problem, it is…
Abstract
This paper addresses the loading/unloading conditions of thediscrete initial—value problem of plastic flow at infinitesimal deformations. As in the continuum problem, it is established that the strain—space formulation of the loading conditions is primary. Generalized trapezoidal and mid‐point rules are discussed. The loading conditions established for the general non‐associated flow problem are shown to naturally reduce to well‐known inequalities for flow rules obeying normality.
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Nielen Stander and Edward L. Wilson
An assessment is made of a 4‐node quadrilateral membrane element with one rotational and two translational degrees of freedom per node, as formulated by Taylor and Simo. The…
Abstract
An assessment is made of a 4‐node quadrilateral membrane element with one rotational and two translational degrees of freedom per node, as formulated by Taylor and Simo. The element, QC9, is formed by degeneration of the 9‐node Lagrange element and condensation of the centre degrees of freedom. An 8‐point, modified reduced integration scheme is implemented in this element, QC9(8), to improve on the 3 × 3 quadrature performance, yet avoid the additional rank deficiency due to reduced integration (2 × 2). QC9(8) performs as good or better than all elements surveyed. It is shown that a similar degeneration of the 16‐node Lagrangian element can be carried out, but that the resulting element fails the patch test.
Rainer Niekamp, Damijan Markovic, Adnan Ibrahimbegovic, Hermann G. Matthies and Robert L. Taylor
The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.
Abstract
Purpose
The purpose of this paper is to consider the computational tools for solving a strongly coupled multi‐scale problem in the context of inelastic structural mechanics.
Design/methodology/approach
In trying to maintain the highest level of generality, the finite element method is employed for representing the microstructure at this fine scale and computing the solution. The main focus of this work is the implementation procedure which crucially relies on a novel software product developed by the first author in terms of component template library (CTL).
Findings
The paper confirms that one can produce very powerful computational tools by software coupling technology described herein, which allows the class of complex problems one can successfully tackle nowadays to be extended significantly.
Originality/value
This paper elaborates upon a new multi‐scale solution strategy suitable for highly non‐linear inelastic problems.
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Fabio De Angelis and Robert L. Taylor
The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the…
Abstract
Purpose
The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.
Design/methodology/approach
An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.
Findings
The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.
Originality/value
In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.
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This “Rapport” proposes to examine the function and effect of British social law in the context of the employment/unemployment debate. This debate is a most significant one for it…
Abstract
This “Rapport” proposes to examine the function and effect of British social law in the context of the employment/unemployment debate. This debate is a most significant one for it has not only British, but also European and International dimensions.
Damijan Markovic, Rainer Niekamp, Adnan Ibrahimbegović, Hermann G. Matthies and Robert L. Taylor
To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications
Abstract
Purpose
To provide a computational strategy for highly accurate analyses of non‐linear inelastic behaviour for heterogeneous structures in civil and mechanical engineering applications
Design/methodology/approach
Adapts recent developments on mathematical formulations of multi‐scale problems to the recently developed component technology based on C++ generic templates programming.
Findings
Provides the understanding how theoretical hypotheses, concerning essentially the multi‐scale interface conditions, affect the computational precision of the strategy.
Practical implications
The present approach allows a very precise modelling of multi‐scale aspects in structural mechanics problems and can play an essential tool in searching for an optimal structural design.
Originality/value
Provides all the ingredients for constructing an efficient multi‐scale computational framework, from the theoretical formulation to the implementation for parallel computing. It is addressed to researchers and engineers analysing composite structures under extreme loading.
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Nielen Stander and Erwin Stein
Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier…
Abstract
Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier onset of instability in the form of a blown‐up response. As a remedy, develops a plane finite beam element based on the Simo‐Vu Quoc formulation for dynamics and integrates it with an energy‐conserving midpoint time‐stepping rule for solving problems in nonlinear dynamics. Shows that this combination produces a consistently stable and accurate dynamic analysis method even for large time steps.
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