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On modeling and optimal design of beam - bridge structures

Pedersen P., Pedersen N. L.

Foundations of Civil and Environmental Engineering

2006

No. 7

273-291

To obtain black and white solutions (material or non-material) penalizations are applied, and due to problems of low density we can see a clear tendency toward solutions which more or less are truss or frame structures. Often, the accuracy of the finite element models for the continuum is then at its limits. For multiple load cases the formulation with a combination of individual load cases is in reality just as simple as for single load cases, but the design solution naturally depends on the selected combination factors, and we can illustrate this by a 3 D bridge example. It is still possible to obtain solutions by simple optimality criterion iterations which to a large extend, are used in this study. At first, the purpose of the presented paper is to make a comparison between optimal designs found by known methods for topology optimization of continuum structures and optimal designs of structures modeled as trusses. For a statically determined truss each bar can be designed independently and therefore must be fully stressed in an optimal design. We want to focus on the basic knowledge which gives an optimality criterion for single load eases with only a single constraint. Truss and continuum examples are analyzed, optimized, and evaluated to get further insight into the influence from the basic modeling, being truss or continuum. Stiffness as well as strength are important aspects of an optimal design.

Constitutive parameters and their evolution

Pedersen P., Tortorelli D.

Control and Cybernetics

1998

Vol. 27, no 2

295--310

The three-dimensional problem of anisotropic evolution is formulated and solved using the tools from optimal design. Basic assumptions are the principle of maximum energy dissipation and a function that relates the damage, as measured by the rate of a constitutive matrix norm, to an effective stress measure. The presentation relies on alternative description for the 21 constitutive parameters and only restrics the constitutive matrix to be semipositive definite.