By Karoly Jarmai, Jozsef Farkas
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Extra resources for Design, Fabrication and Economy of Welded Structures: International Conference Proceedings, 2008
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4, 280-294 Moser, K. & Swoboda, G. (1978). Explicit stiffness matrix of the linearly varying strain trian gular element. Computers & Structures, 8 No. -O. & Strang, G. (2004). A simple mesh generator in matlab. SIAM Review, 4 6 No. 2, 329-345 Snyman, J. A. (1982). A new and dynamic method for unconstrained minimization. Applied Mathematical Modelling, 6 No. 6, 449^162 Snyman, J. A. & Fatti, L. P. (1987). A multi-start global minimization algorithm with dynamic search trajectories. J Optim Theory Appl, 5 4 No.
1 Orthotropic constitutive relation The stiffness matrix K depends explicitly on x through an orthotropic constitutive relation. The elemental stiffness matrices K (x ) are obtained by stacking unidirec tional composite layers on top of each other to construct an elemental laminate. Only a e a 39 DFE2008 Design, Fabrication and Economy of Welded Structures symmetric fibre layups are considered to avoid out of plane effects. Each unidirec tional composite layer pair i has its own fibre orientation described by x which is measured counterclockwise from X\ in the global coordinate system {Xi, X }.
Further the sequence of inner trajectories is terminated if || V / ( x ^ ' ^ ) | | < e or — a;^ ^|| < e . At this termination point the current minimizer x^ ^ and associated function value f{k+i) p j to a global evaluation procedure, which determines the probability of being the global minimum (see Snyman & Fatti (1987) for details). 99. If the target probability is not met, a new random sample point is selected and a new sequence of inner trajectories is initiated. 4 Problem formulation The problem under consideration is the general inequality constrained minimisation problem: Given a cost function T{x), find the minimum T* such that T* = F(x*) = min {f(x) : g(x) < 0 } , (6) as6R" 1 where x e W is a real vector with n components.
