The general problem in topology optimization is correctly formulated as a doublemin mixed integer nonlinear programming (MINLP) problem based on the minimum total potential energy principle. It is proved that for linear elastic structures, the alternative iteration leads to a Knapsack problem, which is considered to be NP-hard in computer science. However, by using canonical duality theory (CDT...

A mesoscopic analytical model of wrinkling of Plain-Woven Composite Preforms (PWCPs) under the bias extension test is presented, based on a new instability analysis. The analysis is aimed to facilitate a better understanding of the nature of wrinkle formation in woven fabrics caused by large in-plane shear, while it accounts for the effect of fabric and process parameters on the onset of wrinkl...

ABSTRACT This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of isotropic plates. In the semi-analytical finite strip approach, all the displacements are postulated by the appropriate shape functions while in the development process of the full-analytical approach, the Von-Karman’s equilibrium equ...

In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V{q), the curve traced out by the system on a constant energy surface minimizes the action given by / y^2{E — V{q))ds where ds is the line element on the constant energy su...

We analyze numerically the mechanisms controlling the spacing of chimneys--channels devoid of solid--in two-dimensional mushy layers formed by solidifying a binary alloy. Chimneys are the principal conduits through which buoyancy effects material transport out of the mushy layer and into the liquid from which it formed. Experiments show a coarsening of chimney spacing; we pursue the hypothesis ...

Abstract. We investigate the form of the Coulomb potential of a point charge in a noncommutative geometry, using a state of minimal dispersion. We find the deviation of the potential at large distances from the point, distinguishing between coordinate distance and measured distance. Defining the “effective” value of an operator as its expectation value in a minimum dispersion state centered at ...

A new systematic iterative analytical procedure is presented to predict the dynamic response of composite sandwich plates subjected to low-velocity impact phenomenon with/without initial in-plane forces. In this method, the interaction between indenter and sandwich panel is modeled with considering the exponential equation similar to the Hertzian contact law and using the principle of minimum p...

A deterministic global optimization algorithm is introduced for locating global mInlmUm potential energy molecular conformations. The proposed branch and bound type algorithm attains finite €-convergence to the global minimum through the successive refinement of converging lower and upper bounds on the solution. These bounds are obtained through a novel convex lowering bounding of the total pot...

The available potential energy of the atmosphere may be defined as the difference between the total potential energy and the minimum total potential energy which could result from any adiabatic redistribution of mass. It vanishes if the density stratification is horizontal and statically stable everywhere, and is positive otherwise. It is measured approximately by a weighted vertical average of...