Showing papers in "International Journal of Computational Engineering Science in 2000"

Finite element modeling of the thermoelastic behavior of functionally graded plates and shells

Abstract: A new thick shell element is used to study the thermoelastic behavior of functionally graded structures made from shells and plates. The element accounts for the varying elastic and thermal properties across its thickness. It also accounts for the thickness change, normal stresses and strains. The nonlinear heat transfer equations governing the through-thickness thermal distribution are treated using the Rayleigh-Ritz method. Prescribed temperatures as well as convection conditions are imposed on both faces of the shell. Three examples involving functionally graded beams, circular plates and spherical shells are examined. The effect of the volume fraction of the constituent materials and the through-thickness integration order are also investigated.

An Agent-Based Netcentric Framework for Multidisciplinary Problem Solving Environments (MPSE)

Abstract: The process of prototyping is part of every scientific inquiry, product design, and learning activity. The new economic realities require the rapid prototyping of manufactured artifacts and rapid solutions to problems with numerous interrelated elements. This, in turn, requires the fast, accurate simulation of physical processes and design optimization using knowledge and computational models from multiple disciplines (multi-physics and multi-scale models) in science and engineering. Thus, the realization of rapid multidisciplinary prototyping is the new grand challenge. In this application scenario the natural computational resource is a "computational grid" that connects the needed distributed hardware and software resources used to simulate the elements of the artifact. Our research goal is to address this application scenario in the context of parallel computing, cluster computing (LAN based computational grids), and Intranet/Internet computational grids. In this document, we describe the initial design of a generic MPSE framework based on a network of computational agents assuming a net-centric run-time support environment. Moreover, we present the realization of this framework for designing a prototype MPSE (GasTurbnLab) for supporting simulations needed for the design of efficient gas turbine engines.

Fine scale analysis of wrinkled membranes

Abstract: The wrinkling of membranes has been a subject of interset at least since the early part of this century. The standard model for analyzing membrane wrinkling is Tension Field theory, which provides a "coarse" model of the wrinkled membrane. The traditional Tension Field theory has an obvious shortcoming: the solution of Tension Field problems implies a surface that is continuously wrinkled, i.e., the number of wrinkles goes to infinity and wrinkle wavelength goes to zero. We note this condition is not physically realized in practical membranes, where the wrinkle wavelength has finite value. In this paper, we discuss the approach to provide the details of wrinkles themselves, i.e., the number, wavelength, and the wave amplitude of the wrinkles based on a robust, physically based wrinkling algorithm and a standard eigenvalue analysis. This "fine" analysis has been experimentally verified on the deformation of a planar sheet subjected to tensile and shear loadings. We then consider the case of a pressurized initially plane circular membrane with elastic boundary restraint. The approach is finally extended to the prediction of wrinkle parameters of an inflated round parachute model.

Modeling shock-induced chemical reactions

Abstract: A computational method is presented for modeling shock-induced chemical reactions (SICR) in multi-material solid powder mixtures. The reacting materials are assumed to be imiscible, which limits the location of the chemical reaction to the material interface between the reactants. This modeling assumption introduces a fundamental difficulty since the product separates the reactants and quenches the reaction. In reality, there is a transport mechanism through the product, however little is known about it other than it doesn't appear to limit the reaction rate. A computational method for overcoming the quenching of the reaction by the product has shown to be promising. It permits distinct descriptions of the particle interfaces and their evolution as the materials within each particle undergo plastic flow, phase transformation, and chemical evolution. An example calculation of the dynamic behavior of the Nb-Si system is presented.

Nonweak/strong solutions of linear and nonlinear hyperbolic and parabolic equations resulting from a single conservation law

Abstract: This paper presents an investigation of the numerical computations of nonweak/strong solutions of linear and nonlinear hyperbolic and parabolic differential and partial differential equations resulting from a single conservation law using C1p-version least squares finite element formulation (LSFEF) and C11p-version space time least squares finite element formulation (STLSFEF) for stationary and time dependent processes. It is demonstrated that with this approach it is possible to compute nonweak/strong solutions in the sense that the computed solutions possess the same orders of continuity in space and time as the strong solutions and satisfy nonweak (or residual) form of the governing differential equations (GDE's). Other benefits of this approach over weak solutions are also discussed and demonstrated. Stationary and time dependent convection-diffusion and Burgers equations are used as model problems.

Nonlinear dynamics for mixed shells with large rotation and elastoplasticity

Abstract: From a more recent and comprehensive perspective, work on the nonlinear dynamic response of plates and shells calls for detailed studies of several important factors. These include the effect of large spatial rotations on the geometric stiffness and inertia operators, the accurate updating procedures for nodal rotations and associated angular velocities and accelerations, as well as material inelasticity (especially for finite strains). Several of these issues are examined here in conjunction with a recently developed mixed finite element formulation for plates and shells. To this end, and restricting the scope to the case of large overall motions but small strains, low-order displacement/strain interpolations are utilized, together with a radial return algorithm (backward-Euler-integration scheme) for plasticity effects. The Newmark implicit scheme has been employed to integrate the semi-discrete equations of motion. A selective set of elastic as well as elasto-plastic problems has been solved to demonstrate the effectiveness and practical utility of the formulation described for plate and shells with arbitrary geometry.

Stress projection, layerwise-equivalent, formulation for accurate predictions of transverse stresses in laminated plates and shells

Abstract: A two-phase scheme for accurate predictions of interlaminar stresses in laminated plate and shell structures has been addressed in this study. A modified superconvergent patch recovery (MSPR) technique has been utilized to obtain accurate nodal in-plane stresses which are subsequently used with the thickness integration of the three-dimensional equilibrium equations to evaluate the transverse shear and normal stresses. Remarkably, the continuity of the resulting interlaminar stresses is automatically satisfied. Such a two-phase scheme has been applied successfully to a simple smeared layer model (SLM), i.e., a low-order quadrilateral hybrid/mixed element (HMSH5). This simple procedure is found to be completely equivalent to the far more computationally expensive alternative approaches, e.g., sophisticated layerwise approach, for flat geometry. A fairly large number of numerical examples have been solved and the results have shown that the proposed scheme is fairly reliable and computationally cost effective.

Coupled conduction-convection problem for an underground duct containing eight insulated cables

Abstract: The coupled heat conduction/convection problem for eight insulating and heat-generating cables in an underground circular tunnel filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The main feature of the solution procedure is that the multi-phases are treated as a single computational domain with unknown interfacial boundary conditions. The temperature distribution in the metal cores, the insulating layers, and in the surrounding air and soil, together with the convective flow pattern are obtained simultaneously. From the profile of the local Nusselt number, which is strongly dependent on the thermal conductivity ratios and weakly dependent on the Rayleigh number, it is concluded that most of the heat transfer takes place via the bottom of the enclosure through a conductive mode.

Efficient computational methods for large-scale structural optimization

Abstract: Structural optimization problems are usually computationally intensive tasks where much of the computing time is spent for the solution of the finite element equations at each optimization step. The objective of this paper is to present efficient domain decomposition methods for handling large-scale shape and topology optimization problems. The methods presented in this work are based on a two-level domain decomposition implementation which is a combination of a primal and a dual domain decomposition method. This method proved to be very efficient in the case of reanalysis problems, which arise very often in structural optimization problems. The numerical tests demonstrate the computational advantages of the proposed methods which become more pronounced in parallel computing environment.

An optimum spacing problem for five chips on a horizontal substrate in an enclosure – natural convection

Abstract: The optimum spacing problem for five heated chips rested on a conductive substrate in a two dimensional enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. It is found that the conventional equi-spaced arrangement is not an optimum option. An optimum thermal performance can be obtained when the center-to-center distances between the chips follow a geometric series. The maximum relative temperature drop in the optimum configuration can be as much as 17% of the equi-spaced arrangement.

A Lagrangian Quadratic Triangular Fluid Finite Element for Fluid-Structure Interaction Problems.

Abstract: A quadratic triangular fluid element based on Lagrangian frame of reference is formulated for solving coupled fluid-structure interaction problems. The mesh-locking behavior due to simultaneous enforcement of the incompressibility and the irrotational constraints are studied in detail. In addition, their relationship to the number of active degrees of freedom and the number of integration points used to evaluate the stiffness matrix is established. It is found that the order of numerical integration used in the evaluation of stiffness matrix has pronounced effect on the element behavior. It is found that for a given mesh the formulated element does not lock in the absence of irrotationality constraints when the stiffness matrix is fully integrated. The same mesh locks when the stiffness matrix is fully integrated and both the constraints are enforced simultaneously. However, when the volumetric stiffness matrix is fully integrated and the rotational stiffness matrix is reduced integrated, the twin constraints are satisfied giving superior performance. The utility of the derived element to solve some coupled fluid-structure interaction problems is demonstrated and the solutions are compared with the available results.

Solution of continuum mechanics problems by gdqem using edq

Abstract: The differential quadrature (DQ) has been generalized and extended which results in the generic differential quadrature (GDQ) and extended differential quadrature (EDQ). The GDQ and EDQ are used to the discrete element analyses of continuum mechanics problems. In this paper, the generalized differential quadrature element method (GDQEM) is used to solve continuum mechanics problems. The EDQ is also used. The element weighting coefficients are calculated by the extended GDQ. The element weighting coefficients for elements having arbitrary configurations can straightly be calculated. Thus the governing differential or partial differential equations, the transition conditions of two adjacent elements and the boundary conditions can be discretized. The overall algebraic equation system can be obtained by assembling all of the discretized equations. This method can convert a generic engineering or scientific problem having an arbitrary domain configuration into a computer algorithm. Certain continuum mechanics problems are solved by this approach. Numerical results prove that the algorithms are efficient.

Computer simulations in the frame of mean-field theory and its application to a surface-reaction-like cellular automaton model

Abstract: Computer simulations are introduced in the frame of site-approximation mean-field rate equations and applied to an A–B2 surface-reaction-like cellular automaton model. There appears the second-order (continuous) transition between B-saturated and steady reactive phase, which fails to be predicted by pure site-approximation mean-field approach. The conclusion is made that such a kinetic behavior may be explained by fluctuations in number space.

Transient response of point-excited submerged ellipsoidal shells using improved transmitting boundaries

Abstract: Transient response of ellipsoidal shells submerged in an acoustic medium subjected to a concentrated Heaviside load at the apex is studied numerically using improved transmitting boundaries. By employing the rigorous Residual Variable Method, the second derivative in the wave equation with respect to the spatial variable extending to infinity is eliminated. The resulting modified equation is an exact boundary condition nonlocal in space requiring modal analysis. The ellipsoidal shell is considered to be enclosed by an artificial spherical truncation surface in the fluid domain on which the improved transmitting boundary condition is used. The effect of the ratio between the two radii of the submerged ellipsoidal shells on the apex deflection and on the hydrodynamic pressure at the apex is investigated. Numerical results obtained by incorporating improved transmitting boundary conditions into the finite element program are presented in graphical forms and discussed.

Response of a single horizontal soil layer using the volterra series in the frequency domain

Abstract: This paper presents the study of the behavior of a soil deposit formed by a single layer subjected to a bedrock excitation strong enough to induce a nonlinear behavior. The soil deposit will be modeled as a Single Degree of Freedom system. The equation of motion that describes the behavior of the system when a seismic wave travels from the bedrock to the surface is developed. The shear modulus and damping ratio of the soil are nonlinear functions of the shear strain. The response of the system is calculated using the proposed method and a nonlinear step-by-step integration scheme. The hysteretic damping model predicts that the dissipation of energy is independent of frequency. The dissipation of energy in soils is practically independent of frequency, and then the hysteretic damping is a better model to describe the soil behavior. If the hysteretic damping model is used, the analysis has to be done in the frequency domain. Up to the third order kernel of the Volterra series in the frequency domain is developed. An inverse Fourier transforms is needed to retrieve the response in the time domain. The examples showed that the HOFRF method could be employed to calculate the response of a single layer soil deposit subjected to a prescribed acceleration of seismic origin strong enough to induce a nonlinear response in the medium.

Distributed optimization of structure using massively parallel computer

Abstract: The computational algorithm for structural optimization that is suitable for massive parallel computer are proposed. Both analysis algorithm and optimization algorithm are paralleled simultaneously, which make it possible to use more processors than the subdivision number of the structure. The 3 dimensional truss problems were solved as examples. For the parallel computation of analysis, it was shown that when the granularity of the computation is small, the efficiency for parallel computation is low, but as the granularity increase, the efficiency also increase. For the parallel computation of the optimization, it was shown that not only the computational model gives high efficiency, but also it often gives better solution, which is closer to global optimal point. Finally both optimization and analysis are computed in parallel, and it was shown that quite high speed up rate can be obtained.