Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 93
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by:
Paper 154
Optimisation of StabilityConstrained Geometrically Nonlinear Shallow Trusses using a Higher Order PathFollowing Method A. Csébfalvi
Department of Structural Engineering, University of Pécs, Hungary , "Optimisation of StabilityConstrained Geometrically Nonlinear Shallow Trusses using a Higher Order PathFollowing Method", in , (Editors), "Proceedings of the Tenth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 154, 2010. doi:10.4203/ccp.93.154
Keywords: stabilityconstrained optimization, shallow trusses, higher order pathfollowing method, hybrid heuristic method.
Summary
In this paper, a higher order pathfollowing method is presented to tackle the structural stability constraints within truss optimisation. The general truss optimization problem is formulated as a discrete or continuous minimal weight design subjected to several constraints which require the computation of the structural response.
The proposed pathfollowing method [1] is based on the perturbation technique of the stability theory [2] and a nonlinear modification of the classical linear homotopy method [3]. The nonlinear function of the total potential energy for conservative systems can be expressed in terms of nodal displacements and the load parameter. The equilibrium equations are given from the principle of the stationary value of the total potential energy. The stability investigation is based on the eigenvalue computation of the Hessian matrix. In each step of the pathfollowing process we get information about the displacement, stresses, local, and global stability of the structure. With the help of the higherorder predictorcorrector algorithm, we are able to compute an arbitrary load deflection path and detect the different type of stability points. During the optimization process, a truss is characterized by its maximal load intensity factor along the equilibrium path. Within the predictor step, an implicit ODE problem and in the corrector phase a nonlinear equation system has to be solved. The firstorder derivative is obtained from the nullspace of the augmented Jacobian matrix. The higher order derivatives need the MoorPenrose pseudoinverse of the augmented Jacobian matrix. The equilibrium path computation terminates if the procedure reaches the applied load level, a singular point or any other constraints violating point on the equilibrium path. In order to demonstrate the viability and the efficiency of the proposed approach computational results are presented using the ANGEL hybrid metaheuristic as the optimization method. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
