Showing papers on "Smoothed finite element method published in 1970"

Finite element method for piezoelectric vibration

Abstract: A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.

A finite element procedure of the second order of accuracy

Abstract: A finite element procedure of the second order of accuracy for solving second order boundary value problems is presented and justified and numerical results are given.

Finite element with high degree of regularity

Abstract: This paper deals with solving two-dimensional variational problems of second- and third-order by the finite element method. To each meshpoint are associated three or six basic functions of class C1 or C2. The expression of the admissible functions on a triangular and rectangular element are given here in a general form which is specially suitable for computation.

Finite elements for geological modelling.

Abstract: SCALE models have often been used to illustrate or gain insight into geological processes1,2. It may now be possible to study full scale models using a digital computer and the finite element method—a method of stress analysis in complex structures developed in the engineering sciences3.

A Numerical Approach For ThermallyCoupled Fluid And Solid Problems In ComplexGeometries

Abstract: Thermal coupling between fluid and solid domains is widely present in industrial applications. The approach implemented relies upon the existing CFD code N3S (see Chabard [1]), which handles the averaged Navier-Stokes system with a finite element technique, and a module named Syrthes which takes care of the heat equation inside the solid using finite elements technique. An explicit scheme, has proven to be very stable to exchange information (temperature or flux) between solid and fluid domains within each time step. The numerical and geometrical de-coupling of solid and fluid domains has numerous advantages and provides good flexibility when handling complex cases. INTRODUCTION In many industrial applications, a thermal coupling exists between a fluid and the solid body by which it is surrounded. Among topics of interest, studied at EDF, thermal shocks arising in piping systems of nuclear plants can be pointed out. These shocks originate from a quick variation of the flow temperature. This may lead to mechanical damages (like cracks). Of course, other fields, like heat exchangers, electrical devices, etc... have to address the same kind of problem. Experimental approaches have been used extensively in the past, but they may become very costly (when dealing with a very hot fluid under high pressure for example). Moreover, they often lack the flexibility needed when a parametric study is desired. On the other hand, with powerful computer facilities now available at affordable cost, numerical approaches become more and more promising to accurately predict thermal phenomena and their effects. Tackling a full size problem requires to handle thermal phenomena in the fluid part, in the solid part and the strong interaction between the two regions. At EDF, sophisticated numerical tools have been developped in the past years to handle fluid problems. The software N3S relies on finite element techniques to solve the averaged Navier-Stokes equations. Unfortunately, wall effects (from the thermal point of view) could only be taken into account in N3S by imposing a wall temperature or a flux. Therefore, thermal fields within solids were not available and thermal inertia caused by the solid wall could not be accounted for. A general purpose conduction module, Syrthes, is now handling the heat equation inside the solid and the thermal coupling between fluid and solid regions. Transactions on Engineering Sciences vol 5, © 1994 WIT Press, www.witpress.com, ISSN 1743-3533

A Combined Boundary Element And FiniteStrip Solution - BSM

Abstract: This paper presents an approach to a solution based on combining the BEM and the Finite Strip Method, taking the advantages of both. The finite strip method is installed into the boundary element method by expanding the unknown parameters in terms of a trigonometric series and evaluating the unknown coefficients of this series. By this method a reduction in computational efforts needed to solve the given problem is achieved, compared with other numerical techniques. It is noted that the finite strip solution gives us a reduction of a semi dimension in the mesh generation and the boundary element method reduces one dimension. A combination of the boundary element method and the finite strip method, so called the Boundary Strip Method - BSM, creates a new powerful numerical method with two advantages over other numerical methods, the first one is a short computation time and the other is a reduction of one and a half dimensions in the mesh generation. Laplace equation was chosen as a test case for the method and the solution is compared with solution of the same problem using both boundary element and finite element solutions.

Matrix equation analysis in the finite element method

Abstract: Since \\V orId War the event of digital computers, together with problems raised bv the ail:plaJlle and rocket industry. stimulated the deyelopment of appropriate up-to-date structural analysis metho ds suiting actual requirements and the available computer technique. Far from applying the methods already known, making use of the possibilities preEcnted by the speed of computer metbods to solve eyer greater problems. they follow instead entirely new ways. The ne'w methods apply the matrix calculuE in a wide range, not only to simplify the 'writing and programming of algorithms as the natural language of computation methods, hut also to present an elegant and concise mathematical treatment. The most widely extended of them is the finite element method, called by some authors the matrix displacement method. ad\\'antageous by its \\'ersatility. Though initially it had heen applied in structural engineering, just as will be here, essentially it suits to any boundary yalue problem that can be described hy partial (or ordinary) differential equations, for arhitrary domains, houndary conditions and loads. It is 'widely applied for yihration, heat transfer and hydraulic prohlems. The disadvantage of the finite element method is that rather small problems require operations 'with quite large matrices, exceeding the capacity of comparatively up-to-date computers, at an important computer time demand. In what follows, the finite element method will he hriefly surveyed and a method 'will be presented, likely to cut computer time and storage capacity for some frequent hut special cases.

Stress analysis using finite element methods

Abstract: The concept of modern general purpose programs for finite element stress analysis is described, taking the MAGIC System as a representative example. Advantages of the general purpose program approach are discussed. Data processing aspects of the development of such programs are observed to overshadow such considerations as the finite element matrix representations. Nevertheless, the library of finite element representations is asserted to continue to provide an important characterization. Thus, a user-oriented description of general purpose programs is presented from the somewhat old-fashioned viewpoint of the finite element library. This description is carried forward on the basis of example problems that collectively establish the problem solving capabilities of general purpose finite element programs for linear stress analysis.

Hybrid Modelling Techniques Using AcousticBoundary And Finite Element Methods

Abstract: Acoustic analysis is becoming more commonplace due to the evolution of suitable analysis techniques and the increase in computational power of affordable computers. For small acoustic problems, i.e., where the region to be modelled is not large numbers of acoustic wavelengths in extent, the two most commonly used methods are finite elements (FE) and boundary elements (BE). These two techniques both have their advantages and disadvantages, depending on the problem to be solved. FE are definitely better if the fluid medium has inhomogeneous properties. BE do not deal as well with natural frequency calculations. For steady state harmonic response the BE method is better at exterior problems. For interior problems, either technique could be used the author's opinion is that FE has the edge. The relative computational advantage of the FE will increase with the ratio of boundary to volume, as the geometry of the problem changes. Ease of mesh creation is another factor to be taken into account.

Axi-symmetric Finite Element Modelling Of InductionMachine End-regions

Abstract: This paper incorporates an axi- symmetric finite element model to describe the machine end-region magnetic field distribution. The finite element model results can then be used in an harmonic equivalent circuit model to predict the machine performance. An end-region finite element model is developed because it is capable of accurately taking account of the non-linear and eddy current effects in the end-region.