Development Of Finite Element Method Research Articles

A review on seismic metamaterials: From natural toartificial structures

<p indent="0mm">In the recent three decades, the breath-taking discoveries of phononic crystals in conjunction with research advances in acoustic metamaterials have far-reaching implications in many science and engineering branches. These new discoveries can be traced to the fundamentals of wave manipulation and wave attenuation, etc., within a very wide frequency spectrum from ultrahigh electromagnetic wave frequency to very low seismic frequency ranges. Inspired by electromagnetic and photonic crystals, these newly designed artificial structures are able to control acoustic/elastic waves at relatively low frequency ranges. In periodic systems, Bloch waves are formed by reflection, refraction and scattering of De Broglie, electromagnetic/light and acoustic/elastic waves. These waves contain marvelous band structures which allow transmission or lead to attenuation. Frequency domains for transmission and attenuation correspond to passbands and stopbands, respectively. There exist many studies that materialize the idea of designing metadevices at will by utilizing wave band behaviors. Generally, the mechanism for forming stopbands contains two parts, i.e., Bragg scattering and local resonance, that can also be used to identify phononic crystals and acoustic metamaterials. Especially, a Bragg scattering type metamaterial prohibits waves with a wavelength of the same order as the lattice constant from propagating through the structure. It results in a large-scale structural dimension for a low frequency bandgap. Comparatively, local resonance type metamaterials allow the generation of bandgaps at low frequency ranges with relatively small dimensions as their properties rely primarily on the local resonance. The study of seismic wave propagation in civil engineering has been reinvigorated due to the new, exciting concept of seismic metamaterials. The spectacular designs provide new approaches to control seismic surface (Rayleigh and Love) and bulk (pressure and shear) waves for civil and structural engineers. This review traces the state-of-the-art developments of seismic metamaterials and establishes a link between photonic crystals at nano/micro scale and seismic metamaterials at macro scale. We present a survey of more recent developments in seismic metamaterials in terms of geometry, physics (i.e., the mechanism for forming stopbands) and experimental approaches which range from natural sources to artificial structures. A variety of mathematical and physics tools can be extended from photonic crystals to seismic megastructures, such as effective media theory, Brillouin zone, reciprocal space, rainbow trapping, etc. The development of finite element methods provides the possibility to simulate and analyze these complex artificial designs numerically. A school of forest trees as natural seismic metamaterials is a focal point in this review, which enables attenuation of seismic waves using natural resources and also inspires the discovery of seismic metasurfaces. For artificial structures, designs are generally made based on locations (i.e., metabarriers and metafoundations) or mechanisms (i.e., Bragg scattering and local resonance mechanism). Some metamaterial-like transformed urbanism or cities are also verified to work as seismic shielding or cloaking. Further, similar to experimental methods in other disciplines, scale model experiments and full-scale experiments have been explored to validate the efficiency of seismic metamaterials in wave attenuation. Although research in phononic crystals is moving towards extreme frontiers, metastructures working at low frequencies with stability, high bearing capacity, high ductility, wide bandgap and efficient attenuation zones remain substantial challenges. Besides soil-structure interactions, the combination of various components of seismic waves, ground conditions, soil properties, effects of groundwater table, structural nonlinearity or other ineluctable factors is yet to be fully considered. Ultimately, the emergence of seismic metamaterials broadens the horizons for seismic isolation and seismic vibration control. This review will help future researchers witness the continuous development of seismic metamaterials and comprehend the current challenges in this promising, potential and exciting research.

Secondary development of finite-element method based on the calculation of scale effect of soil particles

Soil, regarded as a homogeneous continuous medium in the classical soil mechanics, actually comprises mineral particles of different scales and has the basic characteristics of a heterogeneous discontinuous medium. During the deformation, particles of different scales contained in the soil demonstrate diverse deformation states and produce scale effects. At the same time, the rotation of the particles significantly changes the deformation and strength characteristics of the soil and produces a rotation effect. However, the current finite-element calculations are lacking in the calculation methods that take into account the effects of scale and rotation. In the previous work, one of the authors of this paper introduced an intrinsic scale factor and established a constitutive relationship according to the particle scale effect. Based on the constitutive formula of soil particle scale effect, the UEL subroutine of ABAQUS is used to express particle rotation by node rotation, and secondary development of the finite-element calculation program is carried out to solve the specific calculation problem of soil deformation scale effect caused by particle rotation. The results of a verification example involving a round hole display that the stress concentration factor of the hole decreases to a stable value with the increase of the intrinsic scale factor of the particles, which conforms to the influence mechanism of soil particle deformation and basically verifies the reliability of the secondary development program. Furthermore, using the secondary development program to calculate the stability of a slope illustrates that the shear band uncertainty and the element sensitivity in slope instability analysis are eliminated by considering the particle scale effect of the soil.

Duality in Finite Element Exterior Calculus and Hodge Duality on the Sphere

Finite element exterior calculus refers to the development of finite element methods for differential forms, generalizing several earlier finite element spaces of scalar fields and vector fields to arbitrary dimension n, arbitrary polynomial degree r, and arbitrary differential form degree k. The study of finite element exterior calculus began with the $${\mathcal {P}}_r\varLambda ^k$$ P r Λ k and $${\mathcal {P}}_r^-\varLambda ^k$$ P r - Λ k families of finite element spaces on simplicial triangulations. In their development of these spaces, Arnold, Falk, and Winther rely on a duality relationship between $${\mathcal {P}}_r\varLambda ^k$$ P r Λ k and $$\mathring{{\mathcal {P}}}_{r+k+1}^-\varLambda ^{n-k}$$ P ˚ r + k + 1 - Λ n - k and between $${\mathcal {P}}_r^-\varLambda ^k$$ P r - Λ k and $$\mathring{{\mathcal {P}}}_{r+k}\varLambda ^{n-k}$$ P ˚ r + k Λ n - k . In this article, we show that this duality relationship is, in essence, Hodge duality of differential forms on the standard n-sphere, disguised by a change of coordinates. We remove the disguise, giving explicit correspondences between the $${\mathcal {P}}_r\varLambda ^k$$ P r Λ k , $${\mathcal {P}}_r^-\varLambda ^k$$ P r - Λ k , $$\mathring{{\mathcal {P}}}_r\varLambda ^k$$ P ˚ r Λ k and $$\mathring{{\mathcal {P}}}_r^-\varLambda ^k$$ P ˚ r - Λ k spaces and spaces of differential forms on the sphere. As a direct corollary, we obtain new pointwise duality isomorphisms between $${\mathcal {P}}_r \varLambda ^k$$ P r Λ k and $$\mathring{{\mathcal {P}}}_{r+k+1}^-\varLambda ^{n-k}$$ P ˚ r + k + 1 - Λ n - k and between $${\mathcal {P}}_r^-\varLambda ^k$$ P r - Λ k and $$\mathring{{\mathcal {P}}}_{r+k} \varLambda ^{n-k}$$ P ˚ r + k Λ n - k . These isomorphisms can be implemented via a simple computation, which we illustrate with examples.

Research on Parametric Finite Element Analysis Method of Escalator Truss

On the premise of ensuring the structural strength and safety performance of escalator truss, in order to improve the efficiency of design and development of serial escalator truss, a parametric finite element analysis platform for escalator truss is developed by using the secondary development of finite element method and Visual C++ and data interface technology. In this paper, the structural design and strength characteristics of escalator truss with different parameters are studied, and the strength characteristics of escalator truss with maximum boundary load are analysed. The results show that by using the parameterized finite element analysis platform of escalator, users can get the structural strength results of the serialized truss through automatic modelling calculation only by inputting parameters. While satisfying the structural strength of the truss, the analysis process is greatly simplified and the analysis efficiency is improved.

FEM based delamination damage analysis of bonded FRP composite pipe joints

Delamination damage is one of the major type of fractures encountered by laminated FRP structures, greatly effecting their structural stability. Development of finite element method (FEM) based modelling and simulation technique in order to analyze delamination growth in laminated FRP composite made single lap pipe joints, is the prime concern of the present research. Layered solid 185 elements of ANSYS 18.0 has been used for modelling the FRP composite tubes. Ansys Parametric Design Language (APDL) codes have been developed to simulate delaminations and study their effect on interlaminar stresses. Delamination damages have been considered in the ply-interfaces of the composite tubes in the close vicinity of the adhesive layer and their effect on the adhesive mid-layer stresses has been studied. Comparison of delamination damages in the outer and inner tubes on adhesive stresses revealed that damages in the inner tube are more critical as compared to the delaminated outer adherend.

BIOMECHANICS OF PORCINE BRAIN TISSUE UNDER FINITE COMPRESSION

While the developments in finite element method have made it possible to simulate the complex problems in biomechanics, building an accurate constitutive model of living tissues is a major factor in getting reliable finite element analysis (FEA) results. In this study, a set of experiments were performed to test the properties of porcine brain tissue under unconfined uniaxial compression with 20[Formula: see text]s hold time at varied strain levels (10–50%) and strain rates (0.1–1[Formula: see text]s[Formula: see text]). A novel method was developed to build a quasi-linear viscoelasticity (QLV) model. The elastic function and the relaxation function were calculated separately. An Odgen model was adopted to characterize the elastic behavior, while the relaxation response was modeled at six decay rates. A standard to choose the visco parameters was discussed and carried out. The disparity of parameter values in previous models was discussed and explained. It is suggested that this model should be used in the tested loading conditions (relaxation time, strain rate, strain levels).

Avoiding Finite Element Malpractice through Simulation Governance

The finite element (FE) method is used by engineers daily in the design/assessment of components and structures. The number of engineers using such tools is increasing and will increase further with the so-called democratisation of simulation. However, whilst the method might appear easy to use, with highly effective graphical user interfaces, the fundamental fact is that it is approximate and can produce significant errors in the hands of the inexperienced engineer. These errors, if undetected, can compromise a design to such an extent that it becomes unfit for purpose or, even, unsafe. The way to avoid such FE malpractice is through the application of sound simulation governance. The authors have, together, some 70 years’ experience in the application of FE analysis, in the research and development of FE methods and in the education/mentoring of young engineers. They have a longstanding interest in equilibrium FEs, which invoke simulation governance by ensuring that, even for coarse models, certain solution properties essential to the designer are not compromised. Although the authors’ experience comes mostly from the field of structural engineering, the same principles of simulation governance apply equally to other engineering disciplines where numerical simulation is used.

Recent Advances in Finite Element Applications in Artificial Lumbar Disc Replacement

As a new choice for the treatment of degenerative lumbar disease, artificial lumbar disc replacement has been widely used in clinical surgery. The finite element is a very effective method to predict and simulate the surgery effect. The purpose of this paper is to review the applications of finite element in artificial lumbar disc replacement, such as design of artificial lumbar disc prosthesis, risk and effect evaluation of artificial lumbar disc replacement, and assessment of operation methods. Lastly, we discuss the future development of finite element method applied in this field, including personalized design of the prosthesis, postoperative behavior guide, and artificial lumbar disc replacement combined with fusion surgery. In conclusion, as an invaluable complement to biomechanical experiments and clinical studies, the finite element method makes important contributions to our understanding of biomechanics of intervertebral disc, and plays an important role in the field of artificial lumbar disc replacement.

Advances of finite element analysis for elliptic, parabolic and Maxwell interface equations

The development of finite element methods for interface problems in the recent two decades is reviewed with an emphasis on elliptic, parabolic and Maxwell interface problems. We summarize some important results, e.g., regularity, variational forms, discretization schemes, numerical quadrature, interface approxima-fition, and convergence analysis. The state of the art for these problems is described along with the history of developments. Finally, we outline some applications governed by the PDE systems with interfaces.

Research on the Programming of Calculation and Analysis of the Improved Finite Element Method Based on Matlab

Matlab tools are used to improve the programming in the process of calculation and analysis by adopting the continuous and discrete numerical methods developed in modern times with the variational principles and the subdivision interpolation as the basis, so as to implement the finite element analysis of the module, which is one of the most important method to solve the calculation and analysis in the calculation of complex engineering by finite element method. Firstly, according to the development of finite element method, and the characteristics of point process, we analyze the fundamental characteristics of the finite element method. On the basis of this, combined with the Matlab visual programming GUI component, we has designed the improved calculation and analysis programming of finite element method. In order to verify the rationality of the process, triangular unit division method is used to carry out the empirical analysis. And the results show that this method is effective, and has very strong practicability.

The misconception in finite element method and revision from quasi-conforming

The theory and application of present finite element method have misconceptions. These misconceptions include the insufficient understanding of functional space of finite element and the formulation of weak form derivatives. These misconceptions block the development of finite element method, which lead to the difficulty and failure in solving some problems. The theory and application of quasi-conforming finite element method are displayed as a reference. A sequence of functions is defined to demonstrate the functional space of finite element. The independence principle of elements is given to solve the "conforming problem". The polynomial basis rather than "shape function" is emphasized. The formulation of approach functions of finite element is discussed, which should convergence to the corresponding Taylor series. It is proved that the weak form of strain-displacement equation is necessary and sufficient condition of weak form of equilibrium equation. The string net weak derivative is proposed, which expands the connotation of weak form derivative in finite element method.

AC Resistance Factor in One-Layer Form-Wound Winding Used in Rotating Electrical Machines

Analytical calculation of circulating and eddy currents in windings has been under research for almost a century, yet the calculation accuracy has improved slowly. However, over the recent years, the development of finite-element methods (FEM) has boosted the research. A lot of effort has been taken to calculate the ac resistance losses in transformers in the past, whereas rotating electrical machines have received less attention. These models have not taken the end-winding effect into account. In this paper, 2-D FEM results are compared with analytical equations. Based on these results, a more accurate model compared with Dowell's model for single-layer form-wound windings used in electrical machines is developed empirically, and the end winding resistance is analytically taken into account in the results. A maximum error of 5% is achieved in the range of 0–200 Hz for a single-layer form-wound winding.

Refined Nonconforming Finite Element Methods in Couple Stress/Strain Gradient Theory

This paper reviews the recent development of finite element method for the couple stress/strain gradient theory. Based on the second order couple stress/strain gradient theory, the frame of the C0 continuity and C1 continuity finite elements and convergence criterion as enhanced patch test are discoursed in this paper. The enhanced patch test is used to test convergence of weak C1 continuity element and the capability of C0 continuity penalty element for approaching C1 continuity element. Three couple stress penalty elements including 9-DOF triangular element (CST+BT3) and element (ALT+BT3) and 12-DOF 8-note quadrilateral element (MQ8) are adopted to compare the refined nonconforming 18-DOF triangular element (RCT9+RT9) with weak C1 continuity. Numerical results show that the C0 continuity penalty elements (CST+BT3) and (ALT+BT3) and (MQ8) cannot pass enhanced patch test and are unable to approaching the C1 continuity solution. The C1 weak continuity refined element (RCT9+RT9) can pass the enhanced patch test and possesses higher accuracy. In addition, this paper also includes some information of recent patents on the applications of couple stress/strain gradient theory.

NEW ENHANCEMENTS IN THE INVERSE APPROACH FOR THE FAST MODELING OF AUTOBODY STAMPING PROCESS

International Journal of Computational Engineering ScienceVol. 03, No. 04, pp. 355-384 (2002) No AccessNEW ENHANCEMENTS IN THE INVERSE APPROACH FOR THE FAST MODELING OF AUTOBODY STAMPING PROCESSH. NACEUR, Y. Q. GUO and W. GATIH. NACEURLab. Roberval, University of Technology of Compigne, UMR 6066 du CNRS, BP 20529 - 60205, Compigne Cedex, FranceCorresponding author. Search for more papers by this author , Y. Q. GUOLab. of Mechanics, Materials & Structures (GMMS), University of Reims, U.F.R. Sciences E.N., Moulin de la Housse, BP 1039-51687 Reims, France Search for more papers by this author and W. GATILab. Roberval, University of Technology of Compigne, UMR 6066 du CNRS, BP 20529 - 60205, Compigne Cedex, France Search for more papers by this author https://doi.org/10.1142/S146587630200068XCited by:10 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractWith the development of finite element method and computer technology, the complete modeling of the forming of a 3D sheet metal part using incremental approaches is becoming realistic. However, an accurate 3D simulation is usually too time-consuming to be used in the early design stage. One solution is to use simplified Inverse or One Step approaches for the sheet forming modeling. Unfortunately, these methods often based on implicit static algorithms, suffer from convergence problems because of strong non-linearities. In this paper we firstly present several initial guess methods to speed up the convergence of the implicit static solver used in the Inverse Approach, then we present some new techniques for the treatment of vertical walls (balancing, opening, matrix condensing,) which has proven to be essential when dealing with complicated parts. All these improvements have been introduced into our in-house F.E. software REFORM and applied to the drawing of industrial automobile parts. The obtained rapid convergence enables the easy determination of various process parameters for the design of sheet forming process. It is concluded that a good initial solution and the treatment of vertical walls play an important role to speed up the Inverse Approach modeling of autobody stamping processes.Keywords:Deep DrawingInverse Approachinitial solutiongeometric mappingnon-linear resolution FiguresReferencesRelatedDetailsCited By 10Modeling and Optimization in Manufacturing by Hydroforming and StampingHakim Naceur and Waseem Arif27 April 2021Damage Prediction in Metal Forming Process Modeling and Optimization: Simplified ApproachesYing-Qiao Guo, Yuming Li, Boussad Abbès, Hakim Naceur and Ali Halouani4 September 2014A comprehensive blank development method for forming sheet metal partsJianjun Wu, Xin Wu, Liangcai Deng and Hakim Naceur13 December 2013 | The International Journal of Advanced Manufacturing Technology, Vol. 71, No. 5-8An initial solution estimation method based on As‐Rigid‐As‐Possible mesh parameterization for one‐step simulationQiaosheng Liu, Juntong Xi and Zhuoqi Wu29 Mar 2013 | Engineering Computations, Vol. 30, No. 3Damage Prediction in Metal Forming Process Modeling and Optimization: Simplified ApproachesYing-Qiao Guo, Yuming Li, Boussad Abbès, Hakim Naceur and Ali Halouani15 May 2014Analysis and design of hydroformed thin-walled tubes using enhanced one-step methodXavier Elie-dit-cosaque, Mohamed Said Chebbah, Hakim Naceur and Augustin Gakwaya2 August 2011 | The International Journal of Advanced Manufacturing Technology, Vol. 59, No. 5-8A membrane element model with bending modification for one step inverse methodJingxin Na, Jian Jiao, Yakun Yan and Haipeng Liu1 Jun 2011 | Acta Mechanica Solida Sinica, Vol. 24, No. 3An efficient spreading method for sheet metal parts based on outside normalWu Jian‐jun and Yang Han‐ping18 Jul 2008 | Engineering Computations, Vol. 25, No. 5Approche inverse améliorée pour la minimisation du retour élastique de pièces emboutiesSlim Ben-Elechi, Hakim Naceur, Catherine Knopf-Lenoir and Jean-Louis Batoz15 May 2012 | European Journal of Computational Mechanics, Vol. 17, No. 3Moving least squares response surface approximation: Formulation and metal forming applicationsPiotr Breitkopf, Hakim Naceur, Alain Rassineux and Pierre Villon1 Jun 2005 | Computers & Structures, Vol. 83, No. 17-18 Recommended Vol. 03, No. 04 Metrics History KeywordsDeep DrawingInverse Approachinitial solutiongeometric mappingnon-linear resolutionPDF download

Rapid design of corner restraining force in deep drawn rectangular parts

With the development of finite element method and computer technology, the complete modeling of the forming of a 3D sheet metal part is becoming realistic. However, an accurate 3D simulation is usually too time-consuming to be used in the early stage of design. One solution is to model the straight side of a 3D part as a plane strain problem and the corner section as an axisymmetric problem. Unfortunately, the axisymmetric solution often over-predicts the severity of the deformation at the corner and leads to a very conservative design. In this study, a modified axisymmetric model with a center offset is proposed to predict tearing failure in the corner sections of 3D parts. The proposed offset is found to be a function of the center strains, failure height, and tooling/process parameters, including tooling geometry, material properties, friction coefficient, and restraining force provided by the binder. Finite element analyses of both 3D and 2D axisymmetric models for square and rectangular cup forming are utilized to verify the proposed concept and to define the function. Excellent predictions of the failure heights are obtained. The proposed model enables engineers to rapidly specify the right amount of the restraining force in the corner section based on the desired center strains and forming depth. A detailed design algorithm is provided.

Mesh Quality: A Function of Geometry, Error Estimates or Both?

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. A survey of more recent research in the development of finite element methods describes work on anisotropic meshing algorithms, and on providing good error estimates that reveal the relationship between the error and both the mesh and the solution gradients. The reality of solving complex three-dimensional problems is that such indicators are presently not available for many problems of interest. A simple tetrahedral mesh quality measure using both geometrical and solution information is described. Some of the issues in mesh quality for unstructured tetrahedral meshes are illustrated by means of two simple examples.

Recent developments in finite element methods for structural acoustics

The study of structural acoustics involves modeling acoustic radiation and scattering, primarily in exterior regions, coupled with elastic and structural wave propagation. This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics. The cost-effectiveness of finite element methods is composed of several ingredients. Boundary-value problems in unbounded domains are inappropriate for direct discretization. Employing DtN methodology yields an equivalent problem that is suitable for finite element analysis by posing impedance relations at an artificial exterior boundary. Vell-posedness of the resulting continuous formulations is discussed, leading to simple guidelines for practical implementation and verifying that DtN boundary conditions provide a suitable basis for computation. Approximation by Galerkin finite element methods results in spurious dispersion, degrading with reduced wave resolution. Accuracy is improved by Galerkin/least-squares and related technologies on the basis of detailed examinations of discrete errors in simplified settings, relaxing wave-resolution requirements. This methodology is applied to time-harmonic problems of acoustics and coupled problems of structural acoustics. Space-time finite methods based on time-discontinuous Galerkin/least-squares are derived for transient problems of structural acoustics. Numerical results validate the superior performance of Galerkin/least-squares finite elements for problems of structural acoustics. A comparative study of the cost of computation demonstrates that Galerkon/least-squares finite element methods are economically competitive with boundary element methods, the prevailing numerical approach to exterior problems of acoustics. Efficient iterative methods are derived for solving the large-scale matrix problems that arise in structural acoustics computation of realistics configuration at high wavenumbers. An a posteriori error estimator and adaptive strategy are developed for time-harmonic acoustic problems and the role of adaptivity in reducing the cost of computation is addressed.

Interaction of vehicle and terrain results from 10 years research at IKK

The IKK research program comprises: • ⊎ experimental evaluation of terrain data and formulation of analytical models for soil properties • ⊎ development of models for the different soil-wheel interactions • ⊎ development of a highly sophisticated model, ORIS, for off-road interactive simulation of the driver-vehicle-terrain system and the utilization for vehicle development and mission optimization • ⊎ development of finite element methods, e.g. VENUS, and their utilization for multiple terramechanical problems. With these achievements, the team of scientists of the Institute of Automotive Engineering of the University of the Federal Armed Forces, Hamburg (IKK) could contribute essentially to the state of the art. It is the nature of scientific development that problems are recognized to be important and treated by several institutions in the world often at the same time. Also, in the case of the IKK research program, some problems may have been investigated in parallel by others. This indicates the actuality of the research program, and gives the chance for discussion and cooperation between the different scientific groups in the world, to ensure the dissemination of new pieces of knowledge.

Generalized Galerkin Methods for Convection Dominated Transport Phenomena

A brief survey is made of recent advances in the development of finite element methods for convection dominated transport phenomena. Because of the nonsymmetric character of convection operators, the standard Galerkin formulation of the method of weighted residuals does not possess optimal approximation properties in application to problems in this class. As a result, numerical solutions are often corrupted by spurious node-to-node oscillations. For steady problems describing convection and diffusion, spurious oscillations can be precluded by the use of upwind-type finite element approximations that are constructed through a proper Petrov-Galerkin weighted residual formulation. Various upwind finite element formulations are reviewed in this paper, with a special emphasis on the major breakthroughs represented by the so-called streamline upwind Petrov-Galerkin and Galerkin least-squares methods. The second part of the paper is devoted to a review of time-accurate finite element methods recently developed for the solution of unsteady problems governed by first-order hyperbolic equations. This includes Petrov-Galerkin, Taylor-Galerkin, least-squares, and various characteristic Galerkin methods. The extension of these methods to deal with unsteady convection-diffusion problems is also considered.

New directions in computational mechanics

A few areas of computation mechanics are identified in which considerable progress has occurred and continued extension and refinement are anticipated. In particular, some recent results are presented of calculations performed with general purpose large-scale nonlinear finite element programs. Recent progress in the development of finite element methods for fluids is described. Examples of adaptive refinement and “SUPG” type methods are presented. The ideas emanating from finite elements in fluids are now having some impact on solids and structures. Examples of new element technology for kinematically constrained media and space-time formulations in elastodynamics are presented.