The Journal of Strain Analysis for Engineering Design

Experimental and finite element analyses have attributed considerable significance to the role of the prosthetic collar in load transfer to the proximal femur; however, some clinical evidence suggests that collar/calcar contact is unnecessary and detrimental. This study investigates the effects of collared versus collarless prostheses on cement mantle stresses in a model analysis of the proximal femur.

Three-dimensional embedded strain gauging is used in a three-times full-size model of an implanted left femur. Tensor stresses in the cement mantle are derived for a collarless Exeter™ stem, a small and a large medial-collared stem and a full-collared prosthesis. Results show that the collar causes an increase in proximal-medial compressive longitudinal stresses, with other proximal stresses significantly reduced. Subsidence of the stem in the cement mantle is prevented, inducing unfavourable pivoting of the prosthesis about the calcar into varus. The collar type produces only minor additional effects in the mechanism of load transfer.

The analysis suggests that collars may inhibit the prosthesis from attaining long-term secondary stability, by preventing the stem subsidence evident with cemented collarless implants. Derived stresses also illustrate the considerable variation in the mechanism of load transfer between collared and collarless prostheses in both the proximal and distal regions.

In published literature, the strand constructions dealt with have almost invariably involved only wires which are circular in cross-section. There are, however, instances when shaped wires are used in, for example, half-lock and full-lock coil constructions.

The paper reports details of a theoretical model which enables an insight to be gained into various characteristics of axially loaded lock coil ropes. The model is based on an extension of a previously reported orthotropic sheet concept and provides a fairly simple means of estimating wire kinematics, interwire/interlayer contact forces, effective axial stiffnesses and axial hysteresis in axially preloaded locked coil ropes experiencing uniform cyclic axial load perturbations. The theory takes interwire contact deformations and friction into account.

Final numerical results based on theoretical parametric studies on some substantial cables highlight the substantial role that the outermost layer(s) with shaped wires play as regards the overall axial damping capacity of fully bedded-in (old) locked coil ropes, and it is found that (for the same lay angles and outer diameters) axial hysteresis in locked coil ropes is generally higher than spiral strands which are composed of only round wires. This finding may have significant practical implications in terms of the design against dynamic instability of structures supported by such cables.

Indentation of a sandwich beam is analysed as linear elastic bending of the top skin on a rigid-perfectly plastic foundation (the core). The theoretical predictions of fracture load from this simple theory are shown to be in good agreement with experimental results from indentation tests on strips of sandwich panel, with glass-fibre-reinforced plastic skins and foam core, supported on a rigid base.

A numerical study is made of analytical differentiation (AD) and finite difference (FD) approaches to the computation of sensitivity derivatives required in shape design optimization problems. Based on the boundary element method for linear elastostatics, numerical solutions for response and sensitivity analysis are illustrated for the AD technique and the FD schemes with different step sizes. By solving the problem of an annular disc under internal pressure (for which analytical solutions are available), an indication of the absolute level of accuracy achievable by the FD procedure can be obtained. As there are advantages in using the FD technique for shape optimization, it is desirable to check its accuracy and effectiveness compared to the AD approach. An optimization problem based on the annular disc is then formulated and solved using the various analytical, AD and FD sensitivity values to show how the differing accuracies of the derivatives will affect the efficiency and performance of the optimization process, and whether the FD values used are sufficiently accurate for converging upon the correct optimum solution.

An interaction analysis of an axially loaded single pile and pile group with and without a pile cap in a layered soil medium has been investigated using the two-dimensional photoelastic method. A study of the pile or pile group behaviour has been made, varying the pile cap thickness as well as the embedded length of the pile in the hard stratum. The shear stress distribution along the pile-soil interface, non-dimensionalized settlement values of the single pile and the interaction factor for the pile group have been presented. Wherever possible, the results of the present analysis have been compared with available numerical solutions.

This paper deals with shape optimization of three-dimensional elastic bodies. The proposed approach is based on natural design variables and shape functions and utilizes the boundary element method. The design variables are the magnitudes of a set of fictitious loads applied on the structure. Shape optimal design problems based on minimum mean compliance, peak stress minimization and stress constraints are considered. A general method for shape design sensitivity analysis using the material derivative concept and adjoint variable method is used. The sensitivity formula for a general stress constraint imposed over the optimized boundary is derived. Optimal shapes for three-dimensional problems are presented to show numerical applications.

Among several mathematical models for predicting the mechanical response of a helical wire strand to axisymmetric tension and torque derived in the literature over five decades, purely tensile wire linear elastic models have the symmetry of a stiffness matrix. Curiously, in those models where wire bending and torsion terms were included there was a lack of symmetry. In this paper the origin of the lack of symmetry in the earlier models has been identified and a symmetric model developed. The correct generalized strains for this purpose were derived using Wempner's theory and verified using Ramsey's theory. The validity of this model has been verified by comparing its results with that of earlier models and experiments available. This linear elastic symmetric model brings forth the much needed agreement between the global (strand) and the local (wire) responses which should help to simplify considerably the analysis of multi-layer strands and multi-strand wire ropes.