John Bull

Self‐designing structures: a practical approach

Demonstrates the simple but effective application of a standard finite element program (PAFEC), and the associated geometric modelling code (PIGS), to the improvement of the design of an engineering component. The technique adopted involves augmenting material around zones of high stress and removing material in zones of low stress. This evolutionary procedure is related to the behaviour of bones in animals. The essentially two‐step procedure involves; finite element analysis of the preliminary component design using PAFEC; and, definition of a new geometry using PIGS, with selected stress contours giving an indication of the new shape. The technique, which proceeds iteratively, was first tested successfully on some classical academic optimisation problems. Its subsequent application to the industrial problem of a twin chamber pressurised extruded aluminium section, the primary component of an air drying system, resulted in material savings of up to 50 per cent and an associated drop in the maximum von Mises stress of 45 per cent. While this method does not determine the optimal structural form, it does generate substantial improvements in terms of material usage and reduced maximum stresses. It has the advantage that it can be used by any competent engineer with a working knowledge of the strength of materials, finite elements and structural form.

THE DESIGN OF PRECAST CONCRETE PAVEMENTS ON LOW BEARING CAPACITY SUBGRADES

Abstract By using the finite element method and combining it with Westergaards analysis for concrete pavements, a new design method using 2 metre by 2 metre precast concrete pavement units is presented for heavy duty pavements on low bearing capacity subgrades. One design example is included.

The low stress design of welded plates using the self-designing structures approach

Abstract For cover plates welded to base plates, we show that by linking together finite element adaptive techniques, error estimators and stress trajectories, together with our self-designing structures software, we can design a weldment to obtain the minimum stresses in the base plate, the cover plate and the weld. In this way, a specified fatigue life can be obtained. We believe that such a method will produce more efficient design solutions than those derived by traditional approaches.

Adaptive mesh refinement for shells with modified Ahmad elements

This paper presents a simple scheme for the generation of a quadrilateral element mesh for shells with arbitrary three-dimensional geometry. The present mesh generation scheme incorporates a normal mesh generator for generating a mesh in the two-dimensional plane and a specific mapping technique which maps the two-dimensional mesh onto the three-dimensional curved surface. As the mapping is a one-to-one mapping between the mesh in the plane and that on the curved surface, the resulting surface discretization is compatible with the local mesh parameters in two dimensions. This scheme is further combined, both with a sophisticated error estimate determined by using the best guess values of bending moments and membrane and transverse shear forces obtained from a previous solution, and an effective mesh refinement strategy established at an element level in order to complete an adaptive analysis for shell structures. Numerical examples are shown to illustrate the principles and procedure of the present adaptive analysis.

The use of the equivalent single wheel load concept for discrete raft type pavements

Abstract With the increasing use of 2 meter square discrete raft type pavements to replace insitu concrete pavements and flexible pavement materials; it became necessary to assess the infinite pavement assumption, that an equivalent single wheel load could be used to represent the actual multiple wheel loading for pavement analysis. By carrying out a computer analysis the authors found that the raft pavement stresses varied according to the actual multiple wheel load and its position on the raft. Two series of laboratory experiments confirmed the computer results and showed that the concept of a single wheel load equivalent to the multiple wheel load considerably underestimated the pavements life and should not be used for discrete raft type pavement design.

Linear and Non Linear Numerical Analysis of Foundations

A semi-analytical approach is presented for the analysis of three-dimensional ground vibrations induced by trains traveling over a multi-span elevated bridge with pile foundations. The train is modeled as two sets of moving loads, with one accounting for the front wheelsets and the other for the rear wheelsets, the bridge as a series of elastically supported beams, and the ground as a viscoelastic halfspace. By the present semi-analytical technique, the entire vibration problem is divided into three subproblems, each dealing with the dynamic behavior of the superstructure of the bridge, the interaction between the bridge foundations and surrounding soils, and the wave propagation through the halfspace by point sources. Extensive parametric studies were conducted to evaluate the influence of some key parameters on the ground vibrations caused by moving trains. The numerical results indicated that train–bridge resonance can result in drastically amplified ground responses, which decay in an oscillatory manner as the site-to-bridge distance increases. Moreover, there exists a saturation phenomenon in the ground acceleration response spectra when the train speed exceeds a certain limit. In addition, a comparatively lower level of ground vibrations exists for certain combinations of bridge girder span length and train speed, which suggests the existence of some optimal designs for the bridge concerning mitigation of train-induced ground vibrations. Finally, the effect of elastic bearings of the bridge on the ground responses to the moving trains is also studied.

The effect of large subgrade voids on the fatigue life of runways

Abstract This paper assumes that an explosion under a runway causes a large void, a camouflet, to be formed. It considers the effects of a single wheel load moving along the length of the runway and determines the vertical displacement of the runway both with the unfilled void and with the void filled with polystyrene. In particular it considers the effects of the resulting subgrade stresses on the runways fatigue life. It was found that filling the void made little difference to the displacements or to the fatigue life of the runway or subgrade. Once a camouflet has been identified, the authors recommend that the camouflet should be dug out and refilled to improve the runways fatigue life.

A COMPARISON BETWEEN THE STRESSES COMPUTED FOR FINITE SIZED PRECAST CONCRETE PAVEMENT UNITS USING WESTERGAARDS EQUATIONS AND A NUMERICAL DESIGN METHOD

Abstract Westergaards equations are widely used in the design of rigid concrete highway and aircraft pavements. The equations assume that the pavements are either infinite or semi-infinite in extent. Recently, a numerical design procedure using finite elements has been introduced for finite sized precast concrete pavement units [raft units]. The present paper compares the computed stress results from the two methods for the interior loading on a two metre square raft unit. The results show that there is no simple “slab-size correction factor” to correlate the stress output from the two design methods as suggested by other authors. Westergaards analysis should not be used to design finite sized raft units; the numerical design procedure is recommended.

An analytical solution to the design of footway paving flags

Abstract The use of precast concrete paving flags for areas subjected to over-run by heavy goods vehicles is investigated using the finite element method. For the British Standard sizes of paving flags, the induced concrete flexural stress and induced soil stress are determined and related to the standard axle-load and the paving flag support conditions. From these stresses the pavement life expectancy in terms of the number of standard axle over-runs is predicted. A design example is also given.

Finite Elements Adding and Removing Method for Two­ Dimensional Shape Optimal Design

A simple procedure to add and remove material simultaneously along the boundary is developed to optimize the shape of a two dimensional elastic problems and to minimize the maximum von Mises stress. The results for the two dimensional infinite plate with a hole, are lose to the theoretical results of an elliptical boundary and the stress concentration is reduced by half for the fillet problem. The proposed shape optimization method, when compared with existing derivative based shape optimization methods has many features such as simplicity, applicability, flexibiity, computational efficiency and a much better control on stresses on the design boundary.