Showing papers on "Smoothed finite element method published in 1987"

Finite element methods with B-splines

Abstract: Preface 1. Introduction 2. Basic finite element concepts 3. B-splines 4. Finite element bases 5. Approximation with weighted splines 6. Boundary value problems 7. Multigrid methods 8. Implementation Appendix Notation and symbols Bibliography Index.

A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems

Abstract: An SUPG-type finite element method for linear symmetric multidimensional advective-diffusive systems is described and analyzed. Optimal and near optimal error estimates are obtained for the complete range of advective-diffusive behavior.

Finite Element Analysis: From Concepts to Applications

Abstract: The emphasis is on theory, programming and appilications to show exactly how Finite Element Method can be applied to quantum mechanics, heat transfer and fluid dynamics. For engineers, physicists and mathematicians with some mathematical sophistication.

Understanding and implementing the finite element method

Abstract: Preface Part I. The Basic Framework for Stationary Problems: 1. Some model PDEs 2. The weak form of a BVP 3. The Galerkin method 4. Piecewise polynomials and the finite element method 5. Convergence of the finite element method Part II. Data Structures and Implementation: 6. The mesh data structure 7. Programming the finite element method: Linear Lagrange triangles 8. Lagrange triangles of arbitrary degree 9. The finite element method for general BVPs Part III. Solving the Finite Element Equations: 10. Direct solution of sparse linear systems 11. Iterative methods: Conjugate gradients 12. The classical stationary iterations 13. The multigrid method Part IV. Adaptive Methods: 14. Adaptive mesh generation 15. Error estimators and indicators Bibliography Index.

Computational algorithms for FE formulations involving fractional operators

Abstract: This paper considers the development of transient solution algorithms for finite element simulations of viscoelastic problems involving fractional integrodifferential operators. Specifically, numerical approximations are developed for the Grunwald-Liouville-Riemann formalism. This includes establishing formal error estimations. Based on the numerical representations of the fractional operators, implicit, explicit and predictor corrector type transient algorithms are derived for viscoelastic finite element simulations. To illustrate their computational properties, the results of several numerical benchmark experiments are presented. These emphasize the efficiency and stability of the various algorithms developed.

Finite Element Approach to Rotor Blade Modeling

Abstract: The static and dynamic behavior of helicopter blades is investigated using a fmite element approach. This paper focuses on the development of an accurate geometric and structural model of the blade as a first step toward the complete analysis of the aeroelastic problem. A three-dimensional isaparametrie beam element including shear and waroine deformations of a thin-walled beam made of anisotropic material is formulated far arbitrarily . large deflections and rotations. Rotating and non-rotating frequencies far small amplitude vibrations are also presented. The predictions of this model are found in good agreement with experimentally measured deflections and vibration frequencies. Specific advantages of this finite element solution procedure are as follows: the formal derivation of the com~lex nonlinear equations of motion of the problem is not required, all the nonlinear terms are dealt with in a rational fashion bypassing the need for an ordering scheme, the complex struchrral behavior of the blade is accurately modeled, and finally both the undeformed and deformed geometry of the blade as well as other specific details of the rotor configuration are taken into account in a natural fashion.

A simple error estimator in the finite element method

Abstract: Recently, a new class of error indicators and estimators for the finite element methods has been introduced which is particularly easy to implement into existing finite element codes. This paper proves that the new indicators are equivalent to those analysed earlier by Babuska, thus showing that the rigorous mathematical results for the well-known jump indicator apply also for the new ones.

Nonlocal Finite Element Analysis of Strain‐Softening Solids

Abstract: A two-dimensional finite element formulation for imbricate nonlocal strain-softening continum is presented and numerically demonstrated. The only difference from the usual, local finite element codes is that certain finite elements are imbricated, i.e., they regularly overlap while skipping the intermediate mesh nodes. The element imbrication is characterized by generating proper integer matrices that give the numbers of the nodes for each finite element and the numbers of the imbricate elements overlapping each local element. The number of unknown displacements remains the same as for a local finite element code, while the number of finite elements approximately doubles. Numerical results show that stable two-dimensional strain-softening zones of multiple-element width can be obtained, and that the solution exhibits proper convergence as the mesh is refined. The convergence is demonstrated for the load-displacement diagrams, for the strain profiles across the strain-softening band, and for the total energy dissipated by cracking. It is also shown that the local formulations exhibit incorrect convergence; they converge to solutions for which the energy dissipation due to failure is zero, which is physically unacceptable. Stability problems due to strain-softening are avoided by making the loading steps so small that no two mutually nonoverlapping elements may enter the strain-softening regime within the same load step.

Finite element methods for compressible flows

Abstract: The problems of mesh generation and developing effective algorithms for the solution of the equations of compressible flow on unstructured meshes are discussed. Adaptive mesh refinement methods can be implemented in a straightforward manner. Possible adaptive strategies are examined. A finite element method adapted to problems involving high speed compressible flow is described. The adaptive mesh regeneration procedure appears to offer the possibility of large computational savings in three dimensional flow computation.

Toward automatic finite element analysis

Abstract: Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.

Parallel processing in finite element structural analysis

Abstract: A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in finite element computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the finite element analysis process including: 1) formulation level (through the use of mixed finite element models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).

Some Finite Element Methods for Linear Thin Shell Problems

Abstract: This paper is essentially based upon some of our works on numerical analysis of thin shell problems according to Koiter’s equations.

Computational Aspects of the h, p and h-p Versions of the Finite Element Method.

Abstract: : This paper discusses computational complexity of various versions of the finite element method in relation to the achieved accuracy of the finite element solution.

Finite Element Idealization for Linear Elastic, Static, and Dynamic Analysis of Structures in Engineering Practice

Abstract: This report by the Finite Element Idealization Task Committee is a comprehensive aid for modeling structures for finite element analysis. The first part covers static analysis. Aspects of dynamic analysis are covered in the second part. In both parts, separate chapters review basic information on finite element models, analysis methods, preprocessing techniques and postprocessing and interpretation of output results. Separate chapters with specific modeling guidelines are included. This book deals directly with the task of idealization of structures for finite element analysis and the application of general purpose finite element programs to perform complex static and dynamic analysis in engineering practice.

A New Justification of Finite Dynamic Element Methods

Abstract: Finite dynamic element methods were introduced by Premieniecki [11] and were studied by Paz and Dung [10], K.K. Gupta [5, 67, 8, 9], Fricker [2], A.K. Gupta [4] among others.