In this paper we describe the mathematical modelling and computational simulation of the high air pressure (HAP) thermoforming process which is used in the creation of thin walled polymeric structures. This involves, using data from material tests, an elastic-plastic constitutive equation valid for large deformations and a constrained deformation in which there is frictional contact between the polymeric sheet and a constraining surface (the mould surface). Despite a number of simplifying assumptions and some uncertainities in the mathematical model the finite element computations presented predict quite well the actual shape and thickness distribution which are found on sample products.

A general and accurate finite element model for helical springs subject to axial loads (extension or/and torsion) is developed in this paper. Due to the establishment of precise boundary conditions, only a slice of the wire cross-section needs to be modelled; hence, more accurate results can be achieved. An example application to a circular cross-sectional spring is analysed in detail.

A concise finite element model (FEM) of three-layered straight helical wire rope strand under axial loads (tensile and torsional) is presented in this paper. Three-dimensional solid elements were used for structural discretization. The helical symmetry of the strand was used to establish accurate boundary conditions. Contact, friction and plastic yielding were also taken into account. For the global behaviour of wire rope strand, i.e. load vs. strain and load vs. torque (fixed-end) or load vs. strand twist rate (free-end), the finite element results showed better agreement with the experimental results of Utting and Jones (Journal of Strain Analysis for Engineering Design 1988;23(2):79–86) than those calculated using the analytical strand model of Costello (Theory of Wire Rope, 2nd ed. New York: Springer, 1997). In addition, the FE model allows the localised stress distribution to be determined. In particular, this model reveals the non-uniform stress distribution in the outer layer helical wires caused by the trellis point contact. This is particularly relevant in the fixed-end case, where the present analysis predicts an axial tensile rigidity in good agreement with the experimental observations (Utting and Jones), whereas Costello’s model predicts a significantly higher rigidity.

Helically symmetric structures such as helical springs, machine screws and wire rope strands are commonly used structural items. When they are subjected to axial loads (tensile and torsional), these structures may still exhibit the helically symmetric characteristic after loading. If this is the case this feature can be used to substantially simplify the analysis of these structures in numerical simulations. In this paper, the formulation of helically symmetric boundary conditions for finite element (FE) modelling is presented. The helically symmetric relationship is ensured by using constraint equations which relate the displacements of the corresponding nodes on the corresponding artificial boundaries of the model. The application of these helically symmetric equations renders it possible to reduce the finite element model size greatly and improve the accuracy of the results. Examples of a simple circular cross-section bar and wire rope strand are presented which demonstrate the validity of the formulation. Copyright (C) 1999 John Wiley & Sons, Ltd.

A finite element model of a seven-wire strand has been developed for the analysis of termination effects. The cyclic symmetric and antisymmetric features of the strand have been used to reduce the finite element model size. The effects of a fixed-end termination on the contact forces (pressure) and the resulting relative movements between the wires along the contact lines have been determined taking full account of frictional effects in the spiral strands. The aforementioned factors are thought to be strongly related to the fretting fatigue, wear and energy dissipation under cyclic loads.