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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.

The combination method, combined finite element‐boundary element approach, is suitable for unbounded field problems. Although this technique attains a high degree of accuracy, the matrix of the discretized system equation is not banded but sometimes densely or sparsely populated. We reported the development of an infinite boundary element for 2‐D Laplace problems, with which the bandwidth of the discretized system matrix does not increase beyond that of the finite element region. In this paper, we extend this approach and propose another infinite boundary element for 2‐D Helmholtz problems. To illustrate the validity of the proposed technique, some numerical examples are given and their results are compared with those of other methods.

The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in combination with the finite element method. This is sometimes called a combination method and it is suitable as a picture‐frame technique. Although this technique attains good accuracy, the matrix of the discretized equation is not banded, since it is a dense matrix. In this paper, we propose an infinite boundary element which divides the unbounded region radially. By the use of this element, the bandwidth of the discretized system matrix does not increase beyond that of the finite element region and its original matrix structure is maintained. The infinite boundary element can also be applied to homogeneous unbounded field problems, for which the Green's function of the mirror image is difficult to use. To illustrate the validity of the proposed technique, some numerical calculations are demonstrated and the results are compared with those of the usual combination method and the method using the hybrid‐type infinite element.

Infinite elements provide one of the most attractive alternatives for dealing with differential equations in unbounded domains. The region where loads, sources, inhomogeneities and anisotropics exist is modelled by finite elements and the far, uniform region is represented by infinite elements. We propose a new infinite element which can represent any type of decay towards infinity. The element is so simple that explicit expressions can be obtained for the element matrix in many cases, yet large improvements in the accuracy of the solution are obtained as compared with the truncated mesh. Explicit expressions are in fact given for the Laplace equation and 1/rn decay. The element is conforming with linear triangles and bilinear quadrilaterals in two dimensions. The element can be used with any standard finite‐element program without having to modify the shape function library or the numerical quadrature library of the program. The structure or bandwidth of the stiffness matrix of the finite portion of the mesh is not modified when the infinite elements are used. An example problem is solved and the solution found to be better than several other methods in common usage. The proposed method is thus highly recommended.

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

The finite‐element method can be used for an approximate solution of axisymmetric exterior‐field problems by truncating the unbounded domain, or by applying various techniques of coupling a finite region of interest with the remaining far region, which is properly modelled. In this paper, we propose the solution of axisymmetric exterior‐field problems by using the standard finite‐element method in a bounded, transformed domain obtained by conformal mapping from the original, unbounded one. The transformed functionals have very simple expressions and the exact transforms of the original boundary conditions are used in the transformed domain. Consequently no approximation is introduced in the proposed method and improvements in the accuracy of the solution are obtained as compared with several other methods in common usage, especially with the truncated mesh technique. A few example problems are solved and the presented method is found to be simple and computationally highly efficient. It is particularly recommended for problems with material inhomogeneities and anisotropies within large regions.

Materials with anisotropic conductivity are frequently used as sensors in electrical industries. In this paper, an anisotropic conductivity tensor to express Hall effect in n‐type semiconductors is derived and its steady‐current field is solved using the finite element method. Some numerical examples are given and comparison with measured data is discussed.

The paper aims to propose a three‐dimensional (3D) finite element analysis to evaluate the electrical performances of a FBAR (thin‐film bulk acoustic resonator) resonator.

The piezoelectric theory that uses an equivalent circuit is able to evaluate the thickness‐extensional vibration modes in simple 1D configuration but it is not adequate to predict spurious modes with lateral wave vector. Therefore, a fully 3D finite element analysis has been carried out to evaluate the characteristics of a real FBAR prototype that has been fabricated in a research center.

The measured characteristics of the FBAR prototype are compared with simulations obtained by the 3D finite element analysis. The agreement between experimental and numerical results confirms the accuracy of the proposed technique.

The paper proposes a 3‐D numerical approach to design and analyze the electrical characteristics of a real FBAR which has been fabricated following the guidelines obtained by the proposed numerical design.

A technique combining finite elements and boundary elements is promising for unbounded field problems. A hypothetical boundary is assumed in the unbounded domain, and the usual finite element method is applied to the inner region, while the boundary element method is applied to the outer infinite region. On the coupling boundary, therefore, both potential and flux must be compatible. In the finite element method, the flux is defined as the derivative of the potential for which a trial function is defined. In the boundary element method, on the other hand, the same polynomial function is chosen for the potential and the flux. Thus, the compatibility cannot be satisfied unless a special device is considered. In the present paper, several compatibility conditions are discussed concerning the total flux or energy flow continuity across the coupling boundary. Some numerical examples of Poisson and Helmholtz problems are demonstrated.

This paper is concerned with infinite elements for dynamic problems, that is, those which change in time. It is a sequel to our earlier paper on static problems. The paper is in a number of sections. The first is an introduction. In the second the state‐of‐the‐art review of infinite elements is updated. In the third, ‘added mass’ type effects are considered. In the fourth, time dependent problems of the diffusion type, which only involve the first time derivative are considered. Wave problems are considered in the fifth and the necessary radiation conditions for such problems are summarized. Section six deals with dynamic problems of a repetitive nature, that is periodic or harmonic problems. In section seven completely transient problems are dealt with and some fundamental difficulties are noted. Conclusions are drawn in section eight.