Search results

To study and to analyze a second order finite‐element boundary‐flux approximation using isoparametric numerical integration.

The numerical finite‐element integration is the main method used in this research. Since a domain with curved boundary is considered we apply an isoparametric approach. The lumped flux formulation is another method of approach in this paper.

This research study presents a careful analysis of the combined effect of the numerical integration and isoparametric FEM on the boundary‐flux error. Some L₂‐norm estimates are proved for the approximate solutions of the problem under consideration.

The authors offer a general study within the framework of the boundary‐flux approximation theory, which completes the results of published works in this scientific field of research.

A useful application is to employ appropriate quadrature formulae without violating the precision of the boundary‐flux FEM. The lumped mass approximation is also an important practical approach to the problem in question.

The paper presents an entire investigation in FE boundary‐flux approximation theory, in particular, elements of arbitrary degree and domains with curved boundaries. The work is addressed to the possible related fields of interest of postgraduate students and specialists in fluid mechanics and numerical analysis.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

Offshore structures are generally constructed as frameworks of tubular members. The tubular joints should be designed to allow the full post yield or post buckled capacity of the members. However, design guidelines for ultimate strength capacity of these joints are based exclusively upon compilations of test data for simple configurations under simple loading conditions. A methodology based upon the finite element method is presented for analytically predicting the ultimate strength of arbitrary tubular joints. Eight node, isoparametric, curved shell elements were used for the majority of the tubular joint model. Twenty node, isoparametric, solid elements were used to capture the three‐dimensional stress state at the shell intersection while fifteen node, isoparametric, wedge elements modelled the weld profile. Solid‐shell transition elements provided the connection between the three‐dimensional solid elements and the surface based shell elements. Non‐linearities were included via an elastoplastic material model with isotropic strain hardening and the updated Lagrangian approach for finite deflections and rotations. Several experimental tubular joint analyses were reproduced to validate the analytical procedure. Non‐linear finite element analysis was shown to be a practical approach for the evaluation and extension of current design procedures for tubular joints.

Graphical representations play an integral part in the interpretation of the numerical data, resulting from finite element analysis techniques. An algorithm is presented for the efficient mapping of nodal variables derived from isoparametric element formulations, onto a regular Cartesian grid. In addition, a simple and economical technique is described, for the subsequent graphical presentation of the grid values, as a pseudo 3‐dimensional projection, with hidden line removal.

Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials

Finite element meshes can today be used to represent very complex structures because of high performance hardware and software. Although a very successful contributor to modern engineering analysis, such techniques are prone to certain classes of numerical analysis errors which have been long recognized and widely investigated. A more recently recognized source of error has, however, received the attention of analysts, being due to the shape distortion effects of popular types of element, such as isoparametric elements. A mesh scanning program, BERQUAL, part of the BERSAFE system, highlights such potential sources of error, but a more precise assessment is only possible from the final results since element performance depends on the stress gradients in each element. Hence additional error checking using certain stress error measures has been devised and implemented in the post‐processing program PLOTTER, part of the BERSAFE system, to enable rapid, interactive, screen diagnosis. The error measures and implementation details are described and illustrated with suitable examples of progressive shape distortion effects.

Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties.

First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration.

The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy.

New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

Presents a robust and unconditionally stable return‐mapping algorithm based on the discrete counterpart of the principle of maximum plastic dissipation. Develops the explicit expression for the consistent elasto‐plastic tangent modulus. All expressions are derived via tensor formulation showing the advantage over the classical matrix notation. The integration algorithm is implemented in the formulation of the four‐node isoparametric assumed‐strain finite‐rotation shell element employing the Mindlin‐Reissner‐type shell model. By applying the layered model, plastic zones can be displayed through the shell thickness. Material non‐linearity described by the von Mises yield criterion and isotropic hardening is combined with a geometrically non‐linear response assuming finite rotations. Numerical examples illustrate the efficiency of the present formulation in conjunction with the standard Newton iteration approach, in which no line search procedures are required. Demonstrates the excellent performance of the algorithm for large time respective load steps.

A bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view is given. The bibliography at the end of the paper contains 1,726 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1996‐1999.