Showing papers in "International Journal for Numerical Methods in Engineering in 1997"

The Partition of Unity Method

Abstract: A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved This new method can therefore be more efficient than the usual finite element methods An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers The basic estimates for a posteriori error estimation for this new method are also proved © 1997 by John Wiley & Sons, Ltd

Enriched element-free galerkin methods for crack tip fields

Abstract: SUMMARY The Element-Free Galerkin (EFG) method is a meshless method for solving partial di⁄erential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom. ( 1997 by John Wiley & Sons, Ltd.

Tetrahedral mesh improvement using swapping and smoothing

Abstract: Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face- and edge-swapping techniques, which change local connectivity, and optimization-based mesh smoothing methods, which adjust mesh point location. We consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. High-quality meshes are obtained in a computationally efficient manner by using optimization-based smoothing to improve only the worst elements and a smart variant of Laplacian smoothing on the remaining elements. Based on our experiments, we offer several recommendations for the improvement of tetrahedral meshes. © 1997 John Wiley & Sons, Ltd.

The boundary node method for potential problems

Abstract: The Element-Free Galerkin (EFG) method allows one to use a nodal data structure (usually with an underlying cell structure) within the domain of a body of arbitrary shape. The usual EFG combines Moving Least-Squares (MLS) interpolants with a variational principle (weak form) and has been used to solve two-dimensional (2-D) boundary value problems in mechanics such as in potential theory, elasticity and fracture. This paper proposes a combination of MLS interpolants with Boundary Integral Equations (BIE) in order to retain both the meshless attribute of the former and the dimensionality advantage of the latter! This new method, called the Boundary Node Method (BNM), only requires a nodal data structure on the bounding surface of a body whose dimension is one less than that of the domain itself. An underlying cell structure is again used for numerical integration. In principle, the BNM, for 3-D problems, should be extremely powerful since one would only need to put nodes (points) on the surface of a solid model for an object. Numerical results are presented in this paper for the solution of Laplace's equation in 2-D. Dirichlet, Neumann and mixed problems have been solved, some on bodies with piecewise straight and others with curved boundaries. Results from these numerical examples are extremely encouraging. © 1997 by John Wiley & Sons, Ltd.

Shear deformable shell elements for large strains and rotations

Abstract: Well-known finite element concepts like the Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) techniques are combined to derive efficient and reliable finite elements for continuum based shell formulations. In the present study two aspects are covered: The first aspect focuses on the classical 5-parameter shell formulation with Reissner–Mindlin kinematics. The above-mentioned combinations, already discussed by Andelfinger and Ramm for the linear case of a four-node shell element, are extended to geometrical non-linearities. In addition a nine-node quadrilateral variant is presented. A geometrically non-linear version of the EAS-approach is applied which is based on the enhancement of the Green–Lagrange strains instead of the displacement gradient as originally proposed by Simo and Armero. In the second part elements are derived in a similar way for a higher order, so-called 7-parameter non-linear shell formulation which includes the thickness stretch of the shell (Buchter and Ramm). In order to avoid artificial stiffening caused by the three dimensional displacement field and termed ‘thickness locking’, special provisions for the thickness stretch have to be introduced. © 1997 John Wiley & Sons, Ltd.

Viscoplasticity for instabilities due to strain softening and strain-rate softening

Abstract: Three viscoplastic approaches are examined in this paper. First, the overstress viscoplastic models (i.e. the Perzyna model and the Duvaut—Lions model) are outlined. Next, a consistency viscoplastic approach is presented. In the consistency model a rate-dependent yield surface is employed while the standard Kuhn—Tucker conditions for loading and unloading remain valid. For this reason, the yield surface can expand and shrink not only by softening or hardening e⁄ects, but also by softening/hardening rate e⁄ects. A full algorithmic treatment is presented for each of the three models including the derivation of a consistent tangential sti⁄ness matrix. Based on a limited numerical experience it seems that the consistency model shows a faster global convergence than the overstress approaches. For softening problems all three approaches have a regularising e⁄ect in the sense that the initial-value problem remains well-posed. The width of the shear band is determined by the material parameters and, if present, by the size of an imperfection. A relation between the length scales of the three models is given. Furthermore, it is shown that the consistency model can properly simulate the so-called S-type instabilities, which are associated with the occurrence of travelling Portevin-Le Chatelier bands. ( 1997 John Wiley & Sons, Ltd.

A plane stress softening plasticity model for orthotropic materials

Abstract: A plane stress model has been developed for quasi-brittle orthotropic materials. The theory of plasticity, which is adopted to describe the inelastic behaviour, utilizes modern algorithmic concepts, including an implicit Euler backward return mapping scheme, a local Newton-Raphson method and a consistent tangential stiffness matrix. The model is capable of predicting independent responses along the material axes. It features a tensile fracture energy and a compressive fracture energy, which are different for each material axis. A comparison between calculated and experimental results in masonry shear walls shows that a successful implementation has been achieved. © 1997 John Wiley & Sons, Ltd.

Design of energy conserving algorithms for frictionless dynamic contact problems

Abstract: This paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum, angular momentum, and energy in finite element simulations. It is seen that a Lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties. A related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized. This penalty method sacrifices the energy conservation property, but is dissipative under all conditions of changing contact so that the global algorithm remains stable. Notably, it is also shown that augmented Lagrangian iteration utilizing this penalty kernel reproduces the energy conserving (i.e. Lagrange multiplier) solution to any desired degree of accuracy. The result is a robust, stable method even in the context of large deformations, as is shown by some representative numerical examples. In particular, the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations. © 1997 by John Wiley & Sons, Ltd.

A three-dimensional finite element formulation for thermoviscoelastic orthotropic media

Abstract: SUMMARY This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the nite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the nite element solution. Use is made of a Dirichlet{Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. ? 1997 by John Wiley & Sons, Ltd.

Stress points for tension instability in sph

Abstract: In this work, the stress-point approach, which was developed to address tension instability and improve accuracy in Smoothed Particle Hydrodynamics (SPH) methods, is further extended and applied for one-dimensional (1-D) problems. Details of the implementation of the stress-point method are also given. A stability analysis reveals a reduction in the critical time step by a factor of 1/√2 when the stress points are located at the extremes of the SPH particle. An elementary damage law is also introduced into the 1-D formulation. Application to a 1-D impact problem indicates far less oscillation in the pressure at the interface for coarse meshes than with the standard SPH formulation. Damage predictions and backface velocity histories for a bar appear to be quite reasonable as well. In general, applications to elastic and inelastic 1-D problems are very encouraging. The stress-point approach produces stable and accurate results. © 1997 by John Wiley & Sons, Ltd.

a General Topology-Based Mesh Data Structure

Abstract: SUMMARY A representation for a mesh based on the topological hierarchy of vertices, edges, faces and regions, is described. The representation is general and easily supports procedures ranging from mesh generation to adaptive analysis processes. Three implementations are given which concentrate on di⁄erent aspects of performance (storage requirements and speed). Comparisons are made to other published representations. ( 1997 by John Wiley & Sons, Ltd.

Displacement/pressure based mixed finite element formulations for acoustic fluid–structure interaction problems

Abstract: SUMMARY We present reliable finite element discretizations based on displacement/pressure interpolations for the analysis of acoustic fluid—structure interaction problems. The finite element interpolations are selected using the inf-sup condition, and emphasis is given to the fact that the boundary conditions must satisfy the mass and momentum conservation. We show that with our analysis procedure no spurious non-zero frequencies are encountered, as heretofore calculated with other displacement-based discretizations. ( 1997 by John Wiley & Sons, Ltd.

Improved transverse shear stresses in composite finite elements based on first order shear deformation theory

Abstract: A method for calculating improved transverse shear stresses in laminated composite plates, which bases on the first-order shear deformation theory is developed. In contrast to many recently established methods, either higher-order lamination theories or layerwise theories, it is easily applicable to finite elements, since only C0-continuity is necessary and the numerical effort is low. The basic idea is to calculate the transverse shear stresses directly from the transverse shear forces by neglecting the influence of the membrane forces and assuming two cylindrical bending modes. Shear correction factors are no longer required, since the transverse shear stiffnesses are also provided. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show the superiority of the method against using shear correction factors. Furthermore, results obtained with MSC/NASTRAN, which uses a similar but simplified approach, are surpassed.

Recovery by Equilibrium in Patches (rep)

Abstract: A new recovery technique is developed in this paper. It is shown that, for many elements, the behaviour of the method is very similar to that of SPR. Because it does not need to identify super-convergent points, it is applicable for any form of element in which these points are not defined. The formulation is very simple and is based on equilibrating the recovered stresses, in the patch, in the same way that the standard FEM does. This procedure leads to a weak form of equilibrium equations of new stresses on the patch and consequently to answers satisfying the discrete equilibrium conditions. The formulation is consistent with non-linear formulations which iteratively equilibrate the problem. Therefore, this method can be used to project the Gauss points values to nodal points, with minimum disturbance of the global equilibrium. © 1997 by John Wiley & Sons, Ltd.

Finite element modelling of structures including piezoelectric active devices

Abstract: Finite element modelling is used to study the response of plate structures on which piezoelectric active devices are mounted. Such devices are typically small in relation to the size of the structure which can be modelled as a plate or shell structure. In modelling the response of such devices, it is necessary to use a detailed model of the device but to do the same for the whole structure is computationally expensive and unnecessary. Full three-dimensional elements are used to model the piezoelectric devices because such devices are anisotropic, couple electric and elastic fields and satisfy boundary conditions independently on the two fields. Shell elements, approximated by many flat-shell elements are used in modelling the structure. Transition elements have been derived to connect the three-dimensional solid elements in the piezoelectric region to the flat-shell elements used for the plate. This approach has merits in terms of accuracy in modelling the piezoelectric device and computational economy for the plate structure. The use of shell elements is preferred for the structure since brick elements lead to unnatural stiffening of the plate and artificially high natural frequencies. The aspect ratio of the transition elements are first optimized through a numerical study and the sensor and actuator performance of the devices is then verified. © 1997 by John Wiley & Sons, Ltd.

Anisotropic mesh optimization and its application in adaptivity

Abstract: The construction of solution-adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh improvement method of high generality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and that it captures boundary and internal layers in convection-dominated problems. Several important implementation issues are discussed. © 1997 John Wiley & Sons, Ltd.

A parametric study of wave barriers for reduction of train-induced vibrations

Abstract: In this paper, a finite/infinite element scheme developed previously by the authors is employed to investigate the effectiveness of three different wave barriers, i.e., the open trench, in-filled trench, and elastic foundation, in reducing the ground vibrations caused by the passage of trains. The mathematical model adopted herein is the two-dimensional profile that contains the cross-section of the railway, barrier and underlying soils, with the moving train loads simulated as a vertical harmonic line load. Concerning the effect of isolation, the geometric and material parameters of the three barriers investigated include the distance to rail, depth, width and thickness, damping ratio, shear modulus, mass density, Poisson's ratio, elastic modulus, etc. Also examined is the effectiveness of the three barriers with respect to different exciting frequencies. Conclusions are made regarding the selection of optimal parameter values for the three barriers in isolating the train-induced ground vibrations. © 1997 John Wiley & Sons, Ltd.

Static analysis of frame structures by the differential quadrature element method

Abstract: In this paper a new version of Differential Quadrature Method (DQM) is proposed and then extended to analyse frame structures. The new method, called the Differential Quadrature Element Method (DQEM), retains all advantages of the earlier version of the differential quadrature method and overcomes some critical shortcomings existing in the original DQM. The proposed method is, however, different from the Quadrature Element Method (QEM) proposed earlier by Striz et al. The methodology is explained in details herein via a differential quadrature beam element and some numerical examples are given to show the efficiency of the present method. © 1997 by John Wiley & Sons, Ltd.

Voigt-reuss topology optimization for structures with nonlinear material behaviors

Abstract: This work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization. In the proposed framework, alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain. Since two or more materials are permitted to simultaneously occupy local regions of the design domain, small-strain integration algorithms for general two-material mixtures of solids are developed for the Voigt (isostrain) and Reuss (isostress) assumptions, and hybrid combinations thereof. Structural topology optimization problems involving non-linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis (DSA) of energy type functionals are presented. The consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials, elastoplastic materials, and viscoelastic materials. The good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures. It is demonstrated through the second example that structures optimized for maximal strength can be significantly different than those optimized for minimal elastic compliance. © 1997 John Wiley & Sons, Ltd.

Fitting of tabu search to optimize functions of continuous variables

Abstract: SUMMARYTabu Search (TS) is a stochastic global optimization procedure which proved eƒcient to solve variouscombinatorialoptimizationproblems.However,veryfewworksdealwithitsapplicationtoglobalminimiz-ationof functions dependingon continuous variables. The aim of this paper is to proposean adaptation ofTStotheoptimizationofcontinuousfunctions,andtostudytheinsuenceofthemainalgorithmparameterson the convergence towards the optimum. In particular, the application of TS to function optimizationinvolves the deÞnition of the current solution neighbourhood and the management of the tabu list. Theeƒciency of TS applied to continuous global optimization has been tested in detail by using classicalmultimodal functions for which minima are known. ( 1997 by John Wiley & Sons, Ltd. KEY WORDS: tabu search; global optimization; continuous variables 1. INTRODUCTIONThe underlying principles of Tabu Search (TS) were Þrst exposed by Glover.1,2 More recentlyoverviewsaboutTS and itsimplementationin variousÞeldshavebeenproposed,forinstancebyHertz

A coupled heat-moisture transfer theory for deformable unsaturated soil and its algorithmic implementation

Abstract: This paper presents a formulation for coupled heat and moisture transfer in a deformable partially saturated soil. The research is based on a mechanistic phase interaction model coupled to a state surface approach. The method takes into account the coupling effect of temperature gradient and deformations on flows in porous media. Pore water pressure, pore air pressure, temperature and displacement are treated as the primary unknowns. A numerical solution of the formulation is then achieved via the finite element method. An example of the use of the new model is then presented. © 1997 by John Wiley & Sons, Ltd.

Voigt–Reuss topology optimization for structures with linear elastic material behaviours

Abstract: The desired results of variable topology material layout computations are stable and discrete material distributions that optimize the performance of structural systems. To achieve such material layout designs a continuous topology design framework based on hybrid combinations of classical Reuss (compliant) and Voigt (sti) mixing rules is investigated. To avoid checkerboarding instabilities, the continuous topology optimization formulation is coupled with a novel spatial ltering procedure. The issue of obtaining globally optimal discrete layout designs with the proposed formulation is investigated using a continuation method which gradually transitions from the sti Voigt formulation to the compliant Reuss formulation. The very good performance of the proposed methods is demonstrated on four structural topology design optimization problems from the literature. ? 1997 by John Wiley & Sons, Ltd.