Peter M. Pinsky and Raja V. Jasti
A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The…
Abstract
A new laminated composite plate finite element is proposed that is numerically stable and accurate in displacements and stresses, including transverse shear stress. The formulation is based on the Hellinger—Reissner principle with Mindlin kinematics. All stress components are given independent approximations and do not satisfy equilibrium conditions a priori. A novel feature of the formulation is the additive decomposition of the displacement field into two parts corresponding to nodal interpolations and independent local basis functions. The additional basis functions and their associated parameters play an important role in characterizing the accuracy of the element. These functions eliminate shear locking in the lower order elements and provide additional variational constraints on the stresses, leading to very accurate results. A 4‐node and a 9‐node version are developed and it is shown that both elements pass the patch test suggested by Zienkiewicz et al. and are stable in the sense of the Babuška—Brezzi condition. The special structure of the element flexibility matrix provides computational efficiency approaching that of displacement based formulations.
N.R. ALURU, K.H. LAW, P.M. PINSKY and R.W. DUTTON
A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device…
Abstract
A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.
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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…
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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.
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This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE…
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This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.
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P. Ladevèze, L. Arnaud, P. Rouch and C. Blanzé
A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency…
Abstract
A new approach called the “variational theory of complex rays” (VTCR) is developed for calculating the vibrations of weakly damped elastic structures in the medium‐frequency range. Here, the emphasis is put on the most fundamental aspects. The effective quantities (elastic energy, vibration intensity, etc.) are evaluated after solving a small system of equations which does not derive from a finite element discretization of the structure. Numerical examples related to plates show the appeal and the possibilities of the VTCR.
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M.L. Boubakar, L. Boulmane and J.C. Gelin
Addresses the computational aspects involved in the numerical simulation of sheet stamping processes. Focuses on some numerical aspects of the intrinsic complexity of these…
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Addresses the computational aspects involved in the numerical simulation of sheet stamping processes. Focuses on some numerical aspects of the intrinsic complexity of these problems, the first of which is the necessity to take into account properly membrane and bending effects. Presents a well‐adapted shell element. The second aspect concerns the description and the implementation of the initial orthotropic plastic behaviour for sheet metal parts, based on a formulation in a rotating frame using the initial microstructure rotation. The stress calculation algorithm is based on a particular implementation of the elastic predictor‐plastic corrector method. The last aspect concerns the solution procedures with a particular development concerning the treatment of the blankholder load as a constraint. A set of computational results validated with experiments prove the accuracy of the proposed approach in solving stamping problems.
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A. CUITIÑO and M. ORTIZ
We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the…
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We provide a method for automatically extending small‐strain state‐update algorithms and their correspondent consistent tangents into the finite deformation range within the framework of multiplicative plasticity. The procedure, when it applies, operates at the level of kinematics and, hence, can be implemented once and for all independently of the material‐specific details of the constitutive model. The versatility of the method is demonstrated by a numerical example.
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Gonzalo R. Feijóo, Manish Malhotra, Assad A. Oberai and Peter M. Pinsky
The purpose of this paper is to present a method to calculate the derivative of a functional that depends on the shape of an object. This functional depends on the solution of a…
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The purpose of this paper is to present a method to calculate the derivative of a functional that depends on the shape of an object. This functional depends on the solution of a linear acoustic problem posed in an unbounded domain. We rewrite this problem in terms of another one posed in a bounded domain using the Dirichlet‐to‐Neumann (DtN) map or the modified DtN map. Using a classical method in shape sensitivity analysis, called the adjoint method, we are able to calculate the derivative of the functional using the solution of an auxiliary problem. This method is particularly efficient because the cost of calculating the derivatives is independent of the number of parameters used to approximate the shape of the domain. The resulting variational problems are discretized using the finite‐element method and solved using an efficient Krylov‐subspace iterative scheme. Numerical examples that illustrate the efficacy of our approach are presented.
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The time domain BEM/FEM coupling procedure is applied to 2‐D multi‐domain fluid–structure interaction problems. The fluid domain is acoustic and modeled by taking advantage of the…
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The time domain BEM/FEM coupling procedure is applied to 2‐D multi‐domain fluid–structure interaction problems. The fluid domain is acoustic and modeled by taking advantage of the BEM scheme that is suitable to either finite or infinite domains. The structure is modeled by elastodynamic finite elements that can be either linear or nonlinear. The input impact, which can be either plane waves or non‐plane waves, can either be forces acting directly on the fluid–structure system or be explosion sources in the fluid. The far field or near field explosion sources, which are difficult to be simulated for finite element analysis, are very easy to be simulated here by boundary element modeling as internal sources. The stability problem is solved by using the linear θ method, which makes the BEM scheme stable. The numerical results are compared with analytical solutions for two examples.