Elasto-plastic finite element analysis of double chord rectangular hollow section T-joints

Elasto-plastic response of T-joints consisting of double chord, rectangular hollow sections (RHS) has been modelled by treating the chord's mated flanges as thin plates supported by coupled springs that simulate the action of the side walls and bottom flanges. Two loading conditions, namely, branch axial force and branch bending are analyzed. The finite element formulation includes rectangular plate and edge boundary springs in which both in-plane and out-of-plane actions are considered. This paper is an extension of a previous study of the joints' elastic behaviour. Material nonlinearities are incorporated through the Von-Mises yield criterion and its associated flow rule and the Newton-Raphson method is used for the nonlinear analysis. The model is used to determine the ultimate strength and the load-deformation curves for both double and single chord T-joints. The numerical results obtained are in good agreement with some experimental results available in the literature.     

Design of matched bends in rectangular waveguides by finite element method

Waveguide bends of complex geometrical shape frequently occur in microwave systems. To make an accurate prediction of the bend's electrical performances it is useful to employ a general numerical algorithm, such as the finite element method (FEM), which is able to cope with complex geometries. However, since in common practice bends are manufactured either on the E- or H-plane, the FEM can be significantly simplified for these cases, thus enhancing its numerical efficiency. In this article, it is illustrated how the FEM can be simplified and it is shown, by means of several examples, how it can be applied to the case of a straight waveguide which is bent and clamped to obtain low return losses. © 1996 John Wiley & Sons, Inc.     

Separation frequency analysis of interference fitted hollow shaft-hub connections by finite element method

Studies of interference fitted connections show that the traditional design method based on thick-wall cylinder theory has some limitations. Application of the finite element method for the elasto-plastic stress analysis of interference fitted connections gives more complete and accurate results than the traditional method. In this study, stress and separation frequency analyses of interference fitted connections for all preferred diameter series and all preferred hole basis interference fits was carried out. The results showed that the traditional design method was not usable for all thick-walled interference fitting and diameter/interference ratio was decisive for accuracy of results obtained from traditional design methods. For smaller ratio than 750, the results obtained from traditional design method were not viable. The results also showed that designers should pay attention to separation frequencies and decreasing pre-stresses using 100-500 mm of shaft diameters during interference fitting.     

Bending analysis of rectangular moderately thick plates using spline finite element method

A bending analysis of rectangular, moderately thick plates with general boundary conditions is presented using the spline element method. The cubic B spline interpolate functions are used to construct the field function of generalized displacements w, φ_itxand φ_ity. The spline finite element equations are derived based on the potential energy principle. For simplicity, the boundary conditions, which consist of three local spline points, are amended to fit specified boundary conditions. The shear effect is considered in the formulations. A number of numerical examples are described for rectangular, moderately thick plates. Since the cubic B spline interpolate functions have sufficient continuity and are piecewise polynomial, so the present numerical solutions show not only that the method gives accurate results, but also that the unified solutions of thick and thin plates can be directly obtained; the trouble with the so-called shear locking phenomenon does not occur here.     

Superconvergence of mixed finite element methods on rectangular domains

Superconvergence by one power of h along Gauss lines for theBDFM (Brezzi-Douglas-Fortin-Marini) mixed finite element approximation by rectangular elements of the vector field associated with a second order elliptic equation on a rectangular domain is established under an appropriate assumption of smoothness on the exact solution.     

Optimization of least-weight grillages by finite element method

A numerical method is presented for the minimization of the volume of grillages with a stress constraint. The material distribution in the design domain is optimized by a fully-stressed criterion using a finite element method. The densities and orientations of the beams at nodes in grillages are taken as design variables, which vary in the design domain continuously. As intermediate densities are not suppressed in the optimization procedure, numerical instabilities are completely avoided. As a result, the optimal distribution fields of moments, deformation and material are obtained simultaneously. Subsequently the discrete structures are determined from the optimal distribution fields. The optimization procedure is accomplished by the computer program automatically. The capability of the proposed procedure is demonstrated on several classical benchmark problems.     

Vibrations of grids by the finite element method

The finite element method is applied to the free vibration analysis of grids with arbitrary configuration. Grid bars are of solid or thin-walled doubly symmetric cross-section. Stiffness and consistent mass matrices for flexural behavior include the effects of shear deformation and rotary inertia in bending. The torsional behavior of solid sections is approximated by a linear displacement field, and of thin-walled sections, by a cubic. Rotary inertia in torsion is included in both cases and warping inertia, in the latter.

The computer program performs the free vibration analysis starting from the element stiffness and consistent mass matrices. A numerical solution of a thin-walled beam and a parametric solution of an orthogonal and a skew grid with solid and thin-walled bars are presented.     

A rectangular finite element for moderately thick flat plates

This paper presents the development of a straightforward displacement type rectangular finite element for bending of a flat plate with the inclusion of transverse (or lateral) shear effects. The element has 21 degrees of freedom consisting of nine for the lateral displacement of the midplane and 12 for rotations of the normal to the undeformed midplane of the plate (six each for rotations about the x and y axes). The latter are taken as independent of the slopes of the deformed midplane in order to include deformation due to transverse shear. The element is fully conforming and may be orthotropic. At interelement boundaries, the element matches adjacent elements both with respect to lateral displacement of the midplane and the rotations of the normal. Numerical computations for a number of examples are presented. The results show the element to be more flexible than most other finite element models and agree closely with those from a numerical solution of the three dimensional elasticity equations. The results also converge to those from thin plate theory when the thickness to length ratio becomes small or when the transverse shear moduli are artificially increased.     

Modelling of the rolling processes by a 3-D rigid plastic/visco-plastic finite element method with shifted ICCG method

In this paper, the rolling processes were simulated by a 3-D rigid plastic/visco-plastic FEM. The shifted incomplete Cholesky decomposition of the stiffness matrix is combined with the solution of the equations for velocity increment by the conjugate gradient method, termed the shifted ICCG method, is employed to solve these rolling problems. The performance of the algorithm in terms of the number of iterations and friction variation has been analysed. Numerical tests and application in industry verify the validity and stability of the shifted ICCG method.     

A rectangular laminated anisotropic shallow thin shell finite element

This report contains the details of the development of the stiffness matrix for a rectangular laminated anisotropic shallow thin shell finite element. The derivation is done under linear thin shell assumptions. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first-order Hermite interpolation polynomials, it is possible to insure that the displacement state for the assembled set of such elements, to be geometrically admissible. Monotonic convergence of the total potential energy is therefore possible as the modelling is successively refined. The element is systematically evaluated for its performance considering various examples for which analytical or other solutions are available.     

Structural scale modelling by finite element method approach

The structural scale modelling by the finite element method approach is explained. This approach not only has the advantages of the finite element method but also gives insight and ready utility to the modeller. According to the scaling laws obtained by this work, a theoretical example is illustrated to show the workability of the laws. Some practical considerations/limitations of this work are also mentioned. Further extensions to this work, under progress, are also stated.     

Real options pricing by the finite element method

Real option pricing problems in investment project evaluation are mostly solved by the simulation-based methods, the lattice methods and by the finite difference method (FDM). Only a few applications of the finite element method (FEM) to these problems have been reported in the literature; although it seems to be an alternative tool for pricing real options.Unlike the existing finite element-based papers, in this paper we use residual formulation and provide a detailed scheme for practical implementations. The FEM is introduced and developed as a numerical method for real options pricing problems. First of all, a partial differential equation (pde) model is defined, then the problem’s domain is discretized by finite elements. The weak formulation of the pde is then obtained, and finally the solution to the real option pricing problem is found by solving an algebraic system. For benchmarking purposes, the FEM is applied to known investment and abandonment option problems found in the literature and the results are compared with those of some traditional methods. These results show a good performance of the FEM and its superiority over the FDM in terms of convergence, and over the simulation-based methods in terms of the optimal exercise policy.     

Vibration analysis of rectangular mindlin plates by the finite strip method

A finite strip analysis of the vibration of rectangular Mindlin plates with general boundary conditions is described. The normal modes of vibration of Timoshenko beams are used to represent the spatial variation along a strip of the deflection and the two cross-sectional rotations. For the crosswise representation equal-order polynomial interpolation is employed for each of these three basic quantities. The accuracy of the approach is demonstrated by the results of a number of applications to square plates with combinations of simply supported, clamped and free edges.     

Modelling aspects for finite element analysis of ship vibration

The paper describes the present state-of-the-art in analyses of ship vibration and elaborates on the difficulties regarding the finite element modelling.Some suggestions to enable better modelling of the structure, dependent on the aims of the analyses, the accuracy of input data, time and cost are given.It is shown that the main resonant frequencies of global and local structures may be predicted with sufficient accuracy, and a good indication of the forced response level may be obtained at the design stage.     

Elastic-viscoplastic analysis of plates by the finite element method

In this paper the finite element technique is employed in the solution of elastic-viscoplastic plate bending problems. The method is applicable to both thick and thin plates and by attaining steady-state conditions the process offers an alternative method of solution for static elasto-plastic situations. A quadratic isoparametric element based on Mindlin plate theory is adopted and the Euler time-stepping scheme is employed in solution. Yield criteria are based on moment resultants and the Von Mises, Tresca and Johansen forms are included. Several numerical examples are presented and the results compared with those from other sources where available     

Reliability of solutions obtained by the finite element method

The paper examines the conditions when the finite element method produces reliable solutions of applied problems. Specific examples satisfying these conditions are considered.Translated from Kibernetika, No. 3, pp. 23–31, May–June, 1991.     

Convective heat transfer analysis by the finite element method

A numerical procedure based on the finite element method is developed for the analysis of general two-dimensional problems in free/forced convection heat transfer. The dicretization of the field equations through use of the Galerkin method is described. Solution methods for both types of steady state convection are presented.The utility and accuracy of the described method is demonstrated through the solution of diverse examples illustrating both forced and free convection analysis. The use of temperature-dependent material properties and the inclusion of solid body conduction effects are also demonstrated.     

Fundamentals of the finite element method

The present paper gives a brief review of the finite element method. After a historical review, the organization of the finite element analysis in two steps, an element analysis and a system analysis, is described for a simple frame problem.The generalization of this idea to two-and three-dimensional problems is explained and the application of simple types of elements is discussed. The extension to more complex elements is outlined, and finally the capability of the method in solving non-linear and dynamic problems is sketched.     

Periodic tidal flow analysis by finite element perturbation method

The numerical analysis of periodic tidal flow is presented. The present paper investigates a numerical procedure based on the mixed approach of the finite element method and the perturbation method by postulating periodic motion. Several numerical studies are presented to examine the validity of the formulation.