Francesco Ragnedda

Probabilistic-Guaranteed Optimal Design of Membrane Shells Against Quasi-brittle Fracture

Abstract The problems described in this article concern the shape optimization of brittle or quasi-brittle (axisymmetric) elastic shells. The optimization problem takes into consideration the possibilities of cracks arising and consists in finding the shape of the shell loaded by external forces in such a way that the cost function (volume of the shell material) reaches a minimum, while satisfying some prescribed bounds on stress intensity factors. The questions discussed are characterized by incomplete information concerning crack size, crack location, and its orientation. In this context, the article presents some formulations of optimal shell design problems based on probabilistic-guaranteed approach and provides some results of analytical investigation for thin-walled shells with a through cracks.

Some Probabilistic Problems of Beam and Frame Optimization Under Longevity Constraint

Abstract The questions investigated in this article are related to an important class of problems of optimal structural design concerning the shape optimization of quasibrittle elastic bodies with cracks. The optimization problems taken into consideration consist of finding the boundary of a body loaded by cyclic quasistatical forces in such a way that the cost functional (volume of the body) reaches a minimum, while satisfying some prescribed bounds on structural longevity (i.e., on the number of cycles before destruction). These problems are characterized by incomplete information concerning initial crack size and location. In this context, the article presents some possible formulations of optimal structural problems, based on probabilistic approaches, and some examples of analytical solutions.

Multiobjective Approach for Optimal Design of Layered Plates Against Penetration of Strikers

The study deals with the problem of layered plate multiobjective optimization against penetration of strikers having supersonic entry velocities. The plate is monolithic piece-wise homogeneous and composed from several plate-like layers produced from various given materials. The number of considered materials is supposed to be finite and consequently the admissible design set consists of separate discrete values. The impactor is modeled as an axisymmetric rigid body with blunted nose. The ballistic limit velocity and the mass of the plate are taken as components of the vector-functional that is optimized in Pareto sense. Best distribution of given materials is found with the help of genetic algorithm.

Multiobjective Shape Optimization of the Rigid Shell Moving into a Condensed Media

The problem of optimization of rigid bodies moving in the deformable media is considered. The shape of the axisymmetric impactors has been taken as an unknown design variable. The total resistance force, the mass of material, and the volume are taken as components of the minimized vector functional. The formulated multiobjective minimization problem for the vector functional is investigated analytically. As an example, the Pareto-optimal set of optimal shape and the Pareto front are found for the rigid thin-walled axisymmetric shells having the minimum total resistance force and the mass of the shell material.

Several Examples of Application of Nash and Pareto Approaches to Multiobjective Structural Optimization with Uncertainties

The study deals with the problems of optimal structural design with incomplete data concerning applied external loads. The max(guaranteed) approach, based on worst case scenario, is used to take into account these uncertainties. All considered problems are formulated as multiobjective optimization problems. Investigation of the problems of minimization or maximization of vector-criteria is performed analytically with the help of two principally different approaches: Nash-approach and Pareto-approach. Comparison of the procedures of analytical solutions shows the advantages and disadvantages of both approaches. In particular, it was shown that in some shape optimization problems Pareto- and Nash-fronts, containing all optimal solutions of multiobjective optimization problems, are coincident.

Some Optimization Problems for Bodies in Quasi-Steady State Wear#

The problem of optimization of contact interaction of a moving rigid punch and an elastic half-space is investigated taking into account friction and wear. The punch shape is accepted as a desirable design variable and the volumetric wear rate under constraints on the friction dissipation power and the total load, applied to the punch, is taken as an optimized quality criterion. The ratio of the volumetric wear rate and the friction dissipation power under constraint on the total load is also considered as a suitable objective functional. A necessary condition for the optimality in quasi-steady state wear process is derived and discussed. The optimization problem is investigated analytically and exact solutions are obtained for the axysimmetric (stamp) punch which has a circular contact region and moves translationally with a constant velocity or rotates with constant angular velocity.

ON A SHAPE OF AXISYMMETRIC RIGID SHELL MOVING IN DEFORMABLE MEDIUM AND HAVING MINIMAL MASS AND RESISTANCE FORCE

Отыскание формы оболочки вращения минимальной массы и сопротивления рассматривается как задача многокритериальной (многоцелевой) оптимизации. Полная сила сопротивления и масса материала оболочки принимаются в качестве компонент минимизируемого векторного критерия. Форма осесимметричной оболочки играет роль искомой переменной проектирования. Аналитические исследования оптимального решения проводятся с использованием вариационного анализа. Получено точное решение сформулированной многоцелевой задачи оптимизации. Приводятся найденные Паретофронт и величины оптимизируемых функционалов в зависимости от параметров задачи.

Hydroelastic analysis of floating vibrating plate-like structures

ABSTRACT The purpose of this paper is to derive an effective method of analysis of dynamic behavior of plate-like structures interacting with an ideal fluid. We introduce the basic relations describing small harmonic vibrations of elastic plates lying on an ideal fluid and study some essential properties of the corresponding mixed boundary-value problem. A potential noncompressible fluid theory has been used to estimate hydrodynamic forces acting from the fluid outside the plate. An analytical solution of the exterior hydrodynamic problem with two-dimensional plane motions of the plate and of the fluid is derived. The derived analytical expression for hydrodynamic reaction has been taken into the structure equation to derive a closed one-dimensional differential–integral equation of floating structure vibrations. The formulation and the study of the variational problem of vibration analysis for plates interacting with a fluid are performed. The proposed partly analytical approach radically simplifies the analysis problem and minimizes the volume of computations. * Communicated by I. Elishakoff.

Dirichlet problem for the heat equation inh c 1 (dω)

We study a Dirichlet problem for the heat equation in C1-domain D X (0, T) with boundary data in hc1,a subspace of L1.We derive our results using, in the representation of the solution, the kernel function associated to the caloric measure dω