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…
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.
Based on the asymptotic solution for predicted natural frequencies of a two‐dimensional elastodynamic problem from the finite element analysis, presents the concept of the…
Based on the asymptotic solution for predicted natural frequencies of a two‐dimensional elastodynamic problem from the finite element analysis, presents the concept of the asymptotic error, which is an approximate error but tends to the exact error when the characteristic length of elements approaches zero, and a practical error estimator. The present practical error estimator contains two criteria: one is the error estimator criterion, the other the finite element mesh design criterion. Using this practical error estimator, not only can the accuracy of a finite element solution for natural frequencies of a two‐dimensional elastodynamic problem be directly evaluated without any further finite element calculation, but also a new target finite element mesh for the desired accuracy of solution can be immediately designed from the relevant information of an original finite element solution. Generally, for the purpose of designing a new target finite element mesh, this original finite element solution is obtainable from a very coarse mesh of a few elements and usually does not satisfy the accuracy requirement. Since the new target finite element mesh could result in a finite element solution with a desire accuracy, the finite element solution so obtained can be used for a structural design in engineering practice. The related numerical results from vibration problems of three representative plates of different shapes under plane stress conditions have demonstrated the correctness and applicability of the present practical error estimator.
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…
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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.
Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography…
Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.
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…
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.
Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.
Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.
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…
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.
An infinite element based on the doubly asymptotic approximation (DAA) for use in finite element analysis of fluid—structure interactions is presented. Fluid finite…
An infinite element based on the doubly asymptotic approximation (DAA) for use in finite element analysis of fluid—structure interactions is presented. Fluid finite elements model the region near the solid. Infinite elements account for the effects of the outer fluid on the inner region. The DAA‐based infinite elements involve an approximate calculation of the added mass using static mapped infinite elements, plus a consistent damping term. Simple test analyses for a range of fluid properties demonstrate the performance of the solution technique. The analyses of a Helmholtz resonator (open pipe) and a circular plate in water indicate the practical use of the solution approach.
A fixed grid representation of the finite element domain is used to solve elasticity problems. An integration between CAD and FEM systems is made by using this fixed grid representation. Some considerations about FG approximation and stiffness matrix generation are presented. The element stiffness matrix for an element in the mesh is obtained as a factor of a standard element stiffness matrix. A least squares local approximation of stress field is used to calculate the stress at boundary elements. A problem with an analytical solution is used to measure the displacement and stress error. Several meshes and several geometrical configurations of the problem are used to test the reliability of the fixed grid finite element method.