@misc{Wolff2005, type = {Master Thesis}, author = {Wolff, Sebastian}, title = {Implementation und Test eines Optimierungsverfahrens zur Loesung nichtlinearer Gleichungen der Strukturmechanik}, doi = {10.25643/bauhaus-universitaet.727}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-7271}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2005}, abstract = {In displacement oriented methods of structural mechanics may static and dynamic equilibrium conditions lead to large coupled nonlinear systems of equations. In many cases they are solved iteratively utilizing derivatives of Newton's method. Alternatively, the equations may be expressed in terms of the Karush-Kuhn-Tucker conditions of an optimization problem and, therefore, may be solved using methods of mathematical programming. To begin with, the work deals with the fundamentals of the formulation as optimization problem. In particular, the requirements of material nonlinearity and contact situations are analyzed. Proximately, an algorithm is implemented which utilizes the usually sparse structure of the Hessian matrix, whereby particularly the convergence behaviour is analyzed and adjusted. The implementation was tested using examples from statics and dynamics of large systems. The results are verified considering the accuracy comparing alternative solutions (e.g. explicit methods). The potential areas of application is shown and the efficiency of the method is evaluated.}, subject = {Nichtlineare Optimierung}, language = {en} }