TY - CHAP
A1 - Raue, Erich
A1 - Timmler, Hans-Georg
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - NUMERISCHE ANALYSE VON VERBUNDQUERSCHNITTEN MIT NICHTLINEAREM MATERIALVERHALTEN UNTER BERüCKSICHTIGUNG VON VORVERFORMUNGEN
N2 - The presented method for an physically non-linear analysis of stresses and deformations of composite cross-sections and members based on energy principles and their transformation to non-linear optimisation problems. From the LAGRANGE principle of minimum of total potential energy a kinematic formulation of the mechanical problem can be developed, which has the general advantage that pre-deformations excited by shrinkage, temperature, residual deformations after unloading et al., can be considered directly. Thus the non-linear analysis of composite cross-sections with layers of different mechanical properties and different preloading becomes possible and cracks in concrete, stiffness degradation and other specifics of the material behaviour can be taken into account without cardinal modification of the mathematical model. The impact of local defects on the bearing capacity of an entire element can also be analysed in this principle way. Standard computational systems for mathematical optimisation or general programs for spreadsheet analysis enable an uncomplicated implementation of the developed models and an effective non-linear analysis for composite cross-sections and elements.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30039
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Kavrakov, Igor
A1 - Timmler, Hans-Georg
A1 - Morgenthal, Guido
ED - Gürlebeck, Klaus
ED - Lahmer, Tom
T1 - STRUCTURAL OPTIMIZATION USING THE ENERGY METHOD WITH INTEGRAL MATERIAL BEHAVIOUR
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar
N2 - With the advances of the computer technology, structural optimization has become a prominent field in structural engineering. In this study an unconventional approach of structural optimization is presented which utilize the Energy method with Integral Material behaviour (EIM), based on the Lagrange’s principle of minimum potential energy. The equilibrium condition with the EIM, as an alternative method for nonlinear analysis, is secured through minimization of the potential energy as an optimization problem. Imposing this problem as an additional constraint on a higher cost function of a structural property, a bilevel programming problem is formulated. The nested strategy of solution of the bilevel problem is used, treating the energy and the upper objective function as separate optimization problems. Utilizing the convexity of the potential energy, gradient based algorithms are employed for its minimization and the upper cost function is minimized using the gradient free algorithms, due to its unknown properties. Two practical examples are considered in order to prove the efficiency of the method. The first one presents a sizing problem of I steel section within encased composite cross section, utilizing the material nonlinearity. The second one is a discrete shape optimization of a steel truss bridge, which is compared to a previous study based on the Finite Element Method.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Building Information Modeling
KW - Computerunterstütztes Verfahren
KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28065
SN - 1611-4086
ER -