Analysis of unsteady flow through an oscillating structural system is carried out by using consistent penalty function finite element method and Newmark approach for both fluid and solid. Physical variables including displacement, velocity, and acceleration are presented as a function of time to describe movements of the solid system. The resulting flow fields such as velocity vectors and pressure distributions are displayed for various time steps. The shear stress along channel walls and the pressure coefficient versus time are also shown in this paper. The results revealed that motion of the solid body which becomes a moving boundary had a significant influence on the flow fields. In a steady inlet flow, the structural system can be balanced by the fluid force, and steady-state responses for both fluid and solid are then reached for a sufficiently long time.

Numerical investigation on the interaction of a viscous incompressible fluid with a control valve is conducted by using the finite element method and Newmark approach. Variables including displacement, velocity, and acceleration are presented as a function of time to describe movements of the solid system. The velocity vectors, pressure variations, pressure loss coefficients, and energy losses are displayed to reveal the resulting flow fields. It is observed that the motion of the structural element which becomes a moving boundary had a significant influence on the flow fields. In a periodic inlet flow, the motion of the structural system and the resulting flow fields were almost identical for each cycle after the third cycle. The simulated results presented in this paper provide a good description of the induced flow field in a piping system under the effect of a pulsating piston or a wave.

The conventional penalty function finite element model and balancing diffusivity upwind scheme are adopted to simulate shear flows over a surface-mounted obstacle within flow domain. Experimental data and flow visualization made available by previous investigators are used to assess applicability of the present numerical scheme. With a nonuniform grid system, both schemes have been shown to eliminate numerical oscillations that are generated from nonlinear advection. The computational results reveal that strength of recirculating zone behind the wall obstacle is in proportion to width/height ratio of the obstacle, and the pressure loss coefficient increllses rapidly as the ratio is increased.Key Words: Wall ObstacleNumerical OscillationConventional ModelUpwind Scheme

AbstractOwing to the failure of the finite element analyst to employ a properly refined computational model, the accuracy of preliminary finite element computations is often low. Thus, it is useful to introduce a computational procedure for improving the results obtained from a preliminary finite element solution. Such a procedure is presented in this paper. In this procedure the solution error components are decomposed into two parts. One of the error components is assumed to have a long period variation. The other component is assumed to have a short period variation. Multiplicative and additive correction procedures are introduced to iteratively eliminate the two error components. The multiplicative and additive correction procedures are implemented using multi‐level solution techniques.

The two‐dimensional problem of the interaction of periodic incident waves with a hinged inclined barrier is investigated theoretically and numerically in this study. A combination of the finite element method and an eigenfunction expansion procedure is used to obtain numerical solutions to this problem. The transmission characteristics and the effectiveness of a partially floating, inclined breakwater are studied. The effects of variations in the wave period, angle of inclination of the barrier, and the bottom gap are investigated. It is shown that results obtained by the numerical method compare reasonably well with the experimental data and other theoretical solutions.

Problems of shell analysis are often complicated by the existence of edge layer solution components in the total shell solution. A particular type of edge layer solution is considered. This is the cylindrical shell edge layer. A singular perturbation procedure is used to develop finite element shape functions for this problem. These shape functions have a spatial variation which makes them appropriate for edge layer problems. However, they retain an implementable form. A comparison of the accuracy of the singular perturbation edge element to the accuracy of a traditional element is presented.

International Journal for Numerical Methods in EngineeringVolume 26, Issue 12 p. 2623-2643 Article A finite element transitional mesh generation procedure using sweeping functions L. Carter Wellford Jr., L. Carter Wellford Jr. Department of Civil Engineering, University of Southern California, Los Angeles, California, U.S.A.Search for more papers by this authorMark R. Gorman, Mark R. Gorman Department of Civil Engineering, University of Southern California, Los Angeles, California, U.S.A.Search for more papers by this author L. Carter Wellford Jr., L. Carter Wellford Jr. Department of Civil Engineering, University of Southern California, Los Angeles, California, U.S.A.Search for more papers by this authorMark R. Gorman, Mark R. Gorman Department of Civil Engineering, University of Southern California, Los Angeles, California, U.S.A.Search for more papers by this author First published: December 1988 https://doi.org/10.1002/nme.1620261204Citations: 6AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1 W. R. Buell, ‘Mesh generation—A survey’, J. Eng. Indust. ASME, 332–346 (1973). 2 O. C. Zienkiewicz, ‘An automated generation scheme for plane and curved surfaces by isoparametric coordinates’, Int. j. numer. methods eng., 3, 519–538 (1971). 3 H. A. Kamel, ‘A solids mesh generator and results display package’, J. Press. Vess. Technol., 96, 207–217 (1974). 4 W. A. Cook, ‘Body oriented (natural) co-ordinates for generating three dimensional meshes’, Int. j. numer. methods eng., 8, 27–36 (1974). 5 P. Ravat, ‘Use of bivariate spline functions in preprocessors for ship structure design’, Comp. Struct., 6, 369–380 (1976). Citing Literature Volume26, Issue12December 1988Pages 2623-2643 ReferencesRelatedInformation

A finite element formulation for structural problems chaacterized by small bending rigidities is proposed. In this formulation physically appropriate shape functions are developed using singular perturbation methods. These shape functions account for the effects of applied element pressure. The developed shape functions can be used to solve structural problems involving cables, plates, and shells. Numerical results are presented. These numerical results demonstrate the improved behavior of the new shape functions compared to the Hermitian shape functions.

AbstractA simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental‐iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedures.

In this paper, a technique for the dynamic analysis of geometrically nonlinear structures is developed. A Lagrangian function is employed to construct the structural Hamiltonian. The temporal variation of the response is then expressed in terms of the spatial variables through the use of the Hamiltonian function. To demonstrate the proposed technique, the nonlinear vibration of certain axisymmetric shells is analyzed. A variational formulation is presented and implemented by the finite element method. An incremental-iterative scheme is then developed to solve the governing set of discrete equations. Numerical computations are presented for a circular plate and various spherical caps.

AbstractA series of algorithms, to solve the nonlinear algebraic equations resulting from nonlinear finite element models, are proposed. These algorithms involve a selective relaxation of the corrections defined by the modified Newton method. The resulting techniques accelerate the convergence of the modified Newton method. The improved convergence rate is obtained at the expense of a small increase in storage requirements. The results of numerical experiments, on certain nonlinear elasticity problems, are presented to verify the developed techniques.

AbstractIn this paper, free surface flow problems involving large free surface motion are analysed using finite element techniques. In solving these problems a spatially fixed Eulerian mesh is employed, in conjunction with a moving Lagrangian free surface line. The coupling, between the equations valid on the free surface and the equations valid on the fluid domain, is carried out using hybrid finite element techniques. Physical problems involving solitary wave propagation, sloshing dynamics and porous media flow are analysed to demonstrate the developed technique.

Approximation procedures for the solution of two-dimensional convection-diffusion problems are introduced. In these procedures finite-element techniques are utilized. The developed solution algorithms are based on a variational method of matched asymptotic expansions. When these techniques are used in conjunction with standard Galerkin methods, to solve convection-diffusion equations, highly accurate solutions are obtained. Numerical results for certain two-dimensional problems are presented to establish the accuracy of the proposed procedures.

Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

The nonlinear, mixed elliptic hyperbolic equation describing a steady transonic flow is considered. The original equation is replaced by a system of first-order equations that are hyperbolic in time and defined in terms of velocity components. Parabolic regularization terms are added to capture shock wave solutions and to damp iterative solution algorithms. A finite element Galerkin method in space and a Crank-Nicolson finite difference method in iterative time are used to reduce the problem to the solution of a system of algebraic equations. Stability and convergence characteristics of the iterative method are discussed. The numerical implementation of the method is explained, and numerical results are presented.

AbstractA series of finite element algorithms for the calculation of the post‐buckling behaviour of structures are proposed. The algorithms represent a finite element implementation of a variational principle for nonlinear eigenvalue problems. Incremental amplitude solution schemes are defined. Numerical results are presented for the post‐buckling behaviour of specific structures with linear and nonlinear pre‐buckling states.

The problem of free vibration of non-linear structures is considered initially. It is shown that this problem can be represented as a non-linear eigenvalue problem. Variational principles for non-linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non-linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non-linear eigenvalue parameters can be used in modal expansion approximations for the non-linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non-linear circular plate are determined.

In part 1∗∗Comp. Meths. Appl. Mech. Eng. 14 (1978) 377–390. a series of implicit finite element algorithms for the geometrically nonlinear structural problem were proposed. These algorithms were shown to be computationally efficient because they require the solution of a linear system rather than a nonlinear system at each time point. In addition, because of the conservative nature of the algorithms, their stability properties are easily assessed. One algorithm was shown to be unconditionally stable.