Search results

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.

The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry).

This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes.

The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry).

It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.

Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin‐walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently.

In the paper the development of a new fully three‐dimensional piezoelectric hexahedral finite element based on the p‐version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro‐mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated using various static and dynamic test examples.

In the current contribution it is shown that higher order coupled‐field finite elements hold several advantages for smart structure applications. All numerical examples have been found to agree well with previously published results. Furthermore, it is demonstrated that accurate results can be obtained with far fewer degrees of freedom compared to conventional low order finite element approaches. Thus, the proposed finite element can lead to a significant reduction in the overall numerical costs.

To the best of the author's knowledge, no piezoelectric finite element based on the hierarchical‐finite‐element‐method has yet been published in the literature. Thus, the proposed finite element is a step towards a holistic numerical treatment of structural health monitoring (SHM) related problems using p‐version finite elements.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

Presents a procedure for obtaining an improved finite element solution of boundary problems by estimating the principle of exact displacement method in the finite element technique. The displacement field is approximated by two types of functions: the shape functions satisfying the homogeneous differential equilibrium equation and the full clamping element functions as a particular solution of the differential equation between the nodes. The full clamping functions represent the solution of the full clamping state on finite elements. An improved numerical solution of displacements, strains, stresses and internal forces, not only at nodes but over the whole finite element, is obtained without an increase of the global basis, because the shape functions are orthogonal with the full clamping functions. This principle is generally applicable to different finite elements. The contribution of introducing two types of functions based on the principle of the exact displacement method is demonstrated in the solution procedure of frame structures and thin plates.

The importance of vector finite elements for electromagnetic field computation has been extensively demonstrated in the recent literature. In this study we present a systematic approach to the construction of higher order vector shape functions based on dual vector expansions. The methodology presented results in explicit forms for second order elements. Moreover, it reveals the presence of a whole family of vector finite elements depending on the choice of the degrees of freedom and a set of arbitrary parameters.

This paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM).

The model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains.

The presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions.

This paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.

The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.

Incremental sheet forming represents a promising process in the manufacturing of metallic components, particularly its variant known as single point incremental forming (SPIF). The purpose of this paper is to test and validate the results coming from numerical simulation of SPIF processes using the reduced enhanced solid‐shell formulation, when compared to the solid finite elements available in ABAQUS software. The use of SPIF techniques in the production of small batch components has a potential wide application in fields such as rapid prototyping and biomechanical devices.

Incremental forming processes differ from conventional stamping by not using a press and by requiring a lower number of tools, since no dedicated punches and dies are necessary, which lowers the overall production costs. In addition, it shows relative simplicity and flexible setup for complex parts, when compared with conventional technologies. However, the low speed of production and low‐dimensional accuracy levels are still the main obstacles for a wider application of this technique in the context of large production batches.

In this sense, the use of numerical simulation tools based on the finite element method (FEM) can provide a better understanding of the process' peculiarities. However, there are differences on using distinct finite element formulations, regarding accuracy as well as CPU times during simulations, which can be prohibitive in some cases.

Aiming to provide sounding improvements in these two fields (robustness and cost effectiveness of FEM solutions), the present work encloses a preliminary study about some relevant parameters in the FEM simulation of SPIF. Special focus is given to the use of solid‐shell and solid finite elements, for the sake of generality in modelling, as well as implicit solution schemes for the sake of accuracy. Finally, results coming from both experimental data and commercial FEM packages are compared to those obtained by a reliable and cost‐effective solid‐shell finite element formulation developed and implemented by the authors.

This paper gives a review of the finite element techniques (FE) applied in the area of material processing. The latest trends in metal forming, non‐metal forming, powder metallurgy and composite material processing are briefly discussed. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of the paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An appendix included at the end of the paper presents a bibliography on finite element applications in material processing for 1994‐1996, where 1,370 references are listed. This bibliography is an updating of the paper written by Brannberg and Mackerle which has been published in Engineering Computations, Vol. 11 No. 5, 1994, pp. 413‐55.