Shape Sensitivity Analysis and Optimization of Skeletal Structures and Geometrically Nonlinear Solids

Formulations and computational schemes for shape design sensitivity analysis and optimization have been developed for both skeletal structures and geometrically nonlinear elastic solids. The continuum approach, which is based on the weak variational form of the governing differential equation and the concept of the material derivative, plays a central role in such a development. In the first part of this work, the eigenvalue and eigenvector sensitivity equations for skeletal structures are derived with respect to configuration variables of joint and support locations. This derivation is done by the domain method as well as the boundary method. The discrete approach for the eigenvalue and eigenvector sensitivity analysis is also presented for the purpose of numerical comparison. The resultant sensitivity equations are first validated by a cantilever beam for eigenvalue sensitivity analysis and a simply-supported beam for eigenvector sensitivity analysis. The analytical solutions can be easily obtained for both examples. Moreover, the investigation of numerical accuracy and computational efficiency of these sensitivity equations is done with examples of several skeletal structures. The results show that the domain method has an advantage to be both computationally accurate and efficient. Finally, a design optimization of a vibrating beam is presented to investigate the effects of including the support locations and the support stiffness constants as design variables on the design. It is concluded that the support locations and the support stiffness constants are important to improve the quality of design. The second part of this thesis explores the possibility using the Eulerian formulation as the foundation for shape sensitivity analysis and optimization of a new class of design problems in which the performance criteria are defined in the deformed configuration of a geometrically nonlinear elastic solid. The displacement and rotation of this nonlinear elastic solid are assumed to be large while its strain is assumed to be small. Shape sensitivity equations are derived based upon the Eulerian formulation as well as the total Lagrangian formulation for a general functional. A prismatic bar is evaluated analytically to validate these sensitivity equations. A design optimization scheme is then established which uses the Eulerian formulation for analysis as well as sensitivity analysis, to design the shape of a uniformly loaded beam to minimize the area subjected to geometric and stress constraints. The results show that the proposed sensitivity equations and the design scheme work well for this example

Economic evaluation of the spanish port system using the promethee multicriteria decision method

Due to legislation changes during the Nineties, the Spanish Port System has gone through a series of changes that, simultaneous with a period of economic expansion and generalized marine traffic growth, have affected the Port System’s composition, organization and operation. The gradual transformations produced by this context, give shape to a new model of operation for Port Authorities, which now start to be managed under business criteria and procedures of functional autonomy, competition, effectiveness and profit, moving away from State dependency, and at the same time allowing greater participation of regional governments. As a result, general purpose Spanish ports develop their activity in a very competitive market, where self financing and financial sufficiency prevail as high-priority management goals. Our work considers these circumstances from the approach offered by multiple objective decision models, in order to study the performance evolution of Port Authorities, using certain ratios with economic meaning which will allow determining how their relative ranking within the national set has varied. The great variety of available business ratios and the different concepts to analyze give the problem a discrete multicriteria dimension. Thus we have chosen the Promethee method for our analysis, given its results simplicity and easy understanding for the decision agent, the economic interpretation of its parameters, and the stability of its results. In addition, scale effects between different alternatives are eliminated, allowing the possibility of incomparability among them and offering a sensitivity analysis of the effects.

Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}

We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.Comment: 45 pages, 4 figures; several minor revisions, more systematic treatment of subleading shape-function effects, numerical results and tables updated; version to appear in Physical Review

On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification

We present a new approach to convexification of the Tikhonov regularization using a continuation method strategy. We embed the original minimization problem into a one-parameter family of minimization problems. Both the penalty term and the minimizer of the Tikhonov functional become dependent on a continuation parameter. In this way we can independently treat two main roles of the regularization term, which are stabilization of the ill-posed problem and introduction of the a priori knowledge. For zero continuation parameter we solve a relaxed regularization problem, which stabilizes the ill-posed problem in a weaker sense. The problem is recast to the original minimization by the continuation method and so the a priori knowledge is enforced. We apply this approach in the context of topology-to-shape geometry identification, where it allows to avoid the convergence of gradient-based methods to a local minima. We present illustrative results for magnetic induction tomography which is an example of PDE constrained inverse problem

Topology Optimization of Electric Machines based on Topological Sensitivity Analysis

Topological sensitivities are a very useful tool for determining optimal designs. The topological derivative of a domain-dependent functional represents the sensitivity with respect to the insertion of an infinitesimally small hole. In the gradient-based ON/OFF method, proposed by M. Ohtake, Y. Okamoto and N. Takahashi in 2005, sensitivities of the functional with respect to a local variation of the material coefficient are considered. We show that, in the case of a linear state equation, these two kinds of sensitivities coincide. For the sensitivities computed in the ON/OFF method, the generalization to the case of a nonlinear state equation is straightforward, whereas the computation of topological derivatives in the nonlinear case is ongoing work. We will show numerical results obtained by applying the ON/OFF method in the nonlinear case to the optimization of an electric motor.Comment: 20 pages, 7 figure