Topology Optimization of Continuum Structures with Local Stress Constraints

in International Journal for Numerical Methods in Engineering (1998), 43

We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We rst consider relevant stress criteria for porous ... [more ▼]

We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We rst consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank 2 layered materials. Then, on the basis of the theoretical study of the rank 2 microstructures, we propose an empirical model which extends the power penalized sti ness model (also called SIMP for Solid Isotropic Microstructure with Penalization for intermediate densities). In a second part, solution aspects of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an -constraint relaxation of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications. [less ▲]

An automatic remeshing technique for finite element simulation of forming processes

in International Journal for Numerical Methods in Engineering (1990), 30(8), 1503-1525

Modelling coastal/shelf systems with emphasis on long term trends

in International Journal for Numerical Methods in Engineering (1989), 27(1), 113-127

Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second. However, the ... [more ▼]

Hydrodynamic studies of continental seas have been primarily concerned with tides and storm surges and the associated currents which can have velocities as high as several metres per second. However, the period of the dominant tide is only about half a day and the characteristic life time of a synoptic weather pattern is of the order of a few days. The very strong currents which are produced by the tides and the atmospheric forcing are thus relatively transitory and, over time scales of biological interest, they change and reverse so many times that they more or less cancel out, leaving only a small residual contribution to the net water circulation. Mathematical modelling appears at present as the most reliable approach to the determination of the residual circulation and of the long term transport of nutrients and pollutants in the sea. The residual circulation model developed at the GeoHydrodynamics and Environment Research Laboratory of Liège University (GHER) is described and illustrated by its application to the West-European Continental Shelf. Residual flow patterns on the shelf, and in particular in the Irish Sea and the North Sea, are presented and shown to be in excellent agreement with the observations. The results are exploited to estimate the typical routes and times of residence of nutrients and pollutants and the subsequent long term changes in shelf ecosystems and in the Belgian coastal zone. [less ▲]

Variational Principles and the patch test

in International Journal for Numerical Methods in Engineering (1974), 8

The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion ... [more ▼]

The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connexion loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identiification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement - generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomials expansions, allows q systematic construction of so-called "non-conforming" elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive , htbrids, and the lowest degree element (quadratic) is in fact the Morley constant-moment element. Examples are given for higher displacement fields. The case of plate stretching elements can be handles by duality, the difficulties being here associated with the requirements for diffusivity. Non diffusive elements that pass the zero interface virtual worktest can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids, of the type first proposed by T.H.H. Pian. [less ▲]