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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.

This paper is concerned with static problems, i.e. those which do not change with time. Dynamic problems will be considered in a sequel. The historical development of infinite elements is described. The two main developments, decay function infinite elements and mapped infinite elements, are described in detail. Results obtained using various infinite elements are given, followed by a discussion of possibilities and likely developments.

A simple discrete vortex program written in the Occam language for implementation on transputers is presented. The programming methodology and logic are described, with an emphasis on the use of parallel features. Listings of procedures discussed in the text are given.

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous finite element shape functions, with a high confidence in their correctness. This paper gives a tutorial introduction to the REDUCE language and describes how it was used to generate shape function routines.

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.

This paper is concerned with the treatment of fluid‐structure interaction problems. The paper is divided in a number of sections. The first is an introduction to the historical background which lead to the numerical approach being used today. In the second the main factors affecting the numerical treatment of fluid‐structure interaction problems are identified. The next eight sections discuss each of these factors separately. Conclusions are drawn in section eleven.

A one‐dimensional finite element model, associated with a computer code, has been developed to simulate the thermal response of a decomposing glass‐fibre reinforced composite exposed to a fire environment. The numerical model uses a first‐order Arrhenius equation and includes: transient heat conduction; gas mass flux and internal heat convection of decomposition gases; density loss and Arrhenius decomposition of active material into decomposition gases and residual char; and endothermicity of the decomposition process. An empirical formula, obtained from furnace tests, has been applied to the model as the incident heat flux boundary condition at the heated surface. Presents results for the standard thickness of polyester‐based GRP laminate, 10.9mm, for offshore structures. The predicted temperature profiles are in good agreement with experimental temperatures obtained from furnace tests. This model is able to simulate fire performance characteristics for a large range of typical offshore components with different constructions and materials. It will enable accurate predictions of the life‐time of offshore components in severe offshore hydrocarbon fires.

The time domain BEM/FEM coupling procedure is applied to 2‐D multi‐domain fluid–structure interaction problems. The fluid domain is acoustic and modeled by taking advantage of the BEM scheme that is suitable to either finite or infinite domains. The structure is modeled by elastodynamic finite elements that can be either linear or nonlinear. The input impact, which can be either plane waves or non‐plane waves, can either be forces acting directly on the fluid–structure system or be explosion sources in the fluid. The far field or near field explosion sources, which are difficult to be simulated for finite element analysis, are very easy to be simulated here by boundary element modeling as internal sources. The stability problem is solved by using the linear θ method, which makes the BEM scheme stable. The numerical results are compared with analytical solutions for two examples.

The paper presents infinite elements for axisymmetric electrical field problems with open boundaries. The formulation of the elements is so simple that closed‐form expressions for the infinite element matrix are obtained. In order to test the infinite elements, a simple problem, for which an analytical solution exists, is analysed.

A triangular composite element with 15 degrees of freedom is introduced. It is shown that after an appropriate modification of the Zlámal coordinate transformation this element can be employed as a reference element to curvilinear triangular element of class C with nine degrees of freedom. A complete list of the basis functions, together with a procedure for their automatic generation are included.