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Errors of stress numerical integration for cross-sections with straight and curved boundaries

Matuszak A.

Computer Assisted Methods in Engineering and Science

2015

Vol. 22, no. 2

153--176

Internal forces are integrals of stress in a section area. Integrating the stress for an arbitrary cross-section shape and for the nonlinear stress-strain law σ(ε) is tedious and the use of the boundary integral approach can simplify computations. Numerical integration when applied to the computations of such integrals introduces errors in many cases. Errors of numerical integration depend on the adopted integration scheme, the type of σ(ε) and the shape of the cross-section boundary. In the case of adaptive numerical integration what is very important are the properties of the sequence of errors produced by a given integration scheme in the increasing order of the numerical quadrature or the increasing number of subdivisions. This paper analyses errors caused by different integration schemes for the typical σ(ε) either for a straight or curved boundary. Special attention is paid to the properties of the error sequence in each case. The outcome of this paper is important from the viewpoint of the reliability and robustness of the software developed for nonlinear simulations of bar structures.

Frame structure optimization with complex constraints

Szajek K., Łodygowski T.

Foundations of Civil and Environmental Engineering

2010

No. 13

91--115

Modern building industry puts large demands on designers. Generally, both the freedom in design as well as the constant pressure on cost reduction exert a strong influence on the design process. For decades many near optimal solutions have been developed for a wide spectrum of engineering problems. However, these standard solutions are based on a standard building architecture that in many cases prevents implementation of these solutions. Today, a structure with complex geometry, load and boundary conditions can be analyzed using widely available software solutions. Despite the ease of designing structures that fulfill requirements for both ultimate limit state (ULS) and serviceability limit state (SLS), the question of an optimal solution is still open. In this paper two optimization approaches, the genetic algorithm and the Hooke-Jeeves method with their hybrid form, are applied for optimization of steel structures with complex constraints (based on PN-90/B-03200 standard): an example of I - beam section shape forming and designing of three-bay frame profiles. The entire analysis together with the optimization process has been developed in the SOLDIS [10] environment.