The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel displacement. Then, the panel displacement, accounting also for the fluid–structure interaction, is analyzed with the help of the weak form of the governing partial differential equation, using a Galerkin method. In the first part of this paper, we represent the traveling panel by a single partial differential equation in weak form, using an added-mass approximation of the exact fluid reaction. In the second part, we apply a Galerkin method for dynamic stability analysis of the panel, and present an analytical investigation of static stability loss (divergence, buckling) based on the added-mass model.

The translational movement of an elastic web (panel) performing transverse vibrations caused by initial disturbances is considered. It is supposed that the web moving with a constant translational velocity is described by the model of an elastic panel (beam) with supported edges of the examined span. The problem of the optimal suppression of vibrations of a multispan panel (web) supported at discrete points is formulated with consideration of forces applied to the web. In order to solve the optimization problem, we use modern methods developed with the control theory of distributed parameter systems described by partial differential equations.

The translational motion of a thermoelastic beam under transverse vibrations caused by initial perturbations is considered. It is assumed that a beam moving at a constant translational speed is described by a model of a thermoelastic panel supported at the edges of the considered span. The problem of optimal suppression of vibrations is formulated when applying active transverse influences to the panel. To solve the optimization problem, modern methods developed in the theory of control of systems with distributed parameters described by partial differential equations are used.

Some problems of multipurpose analysis and optimization of deformed structures and thin-walled structural elements are studied in this paper under some constraints including incomplete data. The first problem is the multipurpose optimization of layered plate made from given set of materials in context of optimization of ballistic limit velocity. Incomplete data concerning the thickness of layers of optimized multilayered shield structure are taken into account. The Pareto-approach and numerical evolutionary method (genetic algorithm) are used for solving of the considered multipurpose problem. The second problem studied in the paper is the shape optimization problem for rigid punch moving on the surface of elastic half-space, which is solved analytically in multipurpose formulation taking into account friction of contacted surfaces, wear of materials and arising pressure distributions. The relative movement is considered in frame of quasi-static formulation. Formulated optimization problem is studied analytically using the developed decomposition approach and exact solutions are obtained for the punch which has a rectangular contact region and moves translationally with a constant velocity.

The motion of an axisymmetric shell in a deformable solid medium is considered. It is assumed that the medium resistance is described by a two-term expression containing a constant term (the rigidity characteristic) and an inertial term quadratic with respect to the penetration velocity. A model of the impactor penetration with the normal interactions with the resisting medium taken into account is proposed. The membrane forces and the arising stresses are determined for decelerated motions of the impactor.

The study concerns the problem movement of rigid axisymmetric shell (penetrator or striker) in deformed media. The model of thin-walled shell of revolution is formulated and the two-term quadratic expression is used for estimation of the resistance force as a function of striker velocity in high-speed penetration processes. General analytical representations are found for shell acceleration and arising membrane stresses. Dynamical strength analysis is performed and presented in particular cases of axisymmetric shells of dierent shapes.

The optimization problem of shield (protective plate) structure having given thickness and consisting from several layers is considered. It is supposed that these layers are made from different materials with given properties. The order and thicknesses of layers are determined from the condition of maximization of ballistic limit velocity of the high-speed striker penetrating into the plate. The analytical expressions for the ballistic limit velocity and the relations describing the shield structure are derived, the optimal solutions for the given set of materials and different values of problem parameters are obtained. The theoretical estimation of the parameter characterizing the head part of striker is performed. Keywords: optimization, penetration, layered structures.

Problems of optimal design of piece-wise homogeneous layered plates consisting from different materials against penetration of absolutely rigid strikers are considered. The number of materials is assumed to be finite and consequently the set of admissible design variables is composed from discrete values. Various axisymmetric bodies having cylindrical, conical and truncated conical nose parts are considered as rigid strikers. Problems of finding of optimal layered plate structures providing the maximal ballistic limit velocity and minimal mass are solved using evolutionary method of global extremum search (genetic algorithm). Keywords: multiobjective optimization, penetration in deformable media, layered structures.

The problem of contact pressure optimization is formulated for the case of rigid punch interacted with elastic medium. Coupling of the punch penetration and action of external loads at the outside regions is taken into account. The shape of the punch is considered as an unknown design variable. The minimized integral functional characterizes the discrepancy between the actual contact pressure and the required pressure distribution. The problem is studied under condition that the total forces and moments applied to the punch and the loads acted at the outside regions are given. It is shown that the considered optimization problem can be split and transformed to two successively solved problems. Optimal shapes are found analytically for the punches having rectangular contact domains.

We consider the optimal design problem for cantilever beams of variable rigidity loaded at the free end by an arbitrary transverse force. The value of the cantilever free end vertical displacement serves as the optimality criterion, and the distribution of the cantilever thicknesses (cross-sections) is usually used as the design variable. We present results of an asymptotic analysis and a numerical solution of the optimization problem and discuss specific features of the formation of optimal solutions under nonlinear bending.

The problems of a rigid stamp shape optimization are investigated taking into account the interaction of the stamp with an elastic medium. The external forces applied to the elastic medium are considered as random values having given statistic characteristics. The optimal shapes are found for the stamps having circular shape in plan. Key words: structural optimization, contact interaction, probabilistic approach.

Questions described in this paper are concerned with the shape optimization of brittle or quasi-brittle (axisymmetric) elastic shells. These questions take into consideration the possibilities of crack arising and damage accumulation in the process of application of cyclic load to the shell structure. Initial structural defects, arising cracks and damage accumulation are characterized by incomplete information concerning initial crack sizes, crack position and its orientation. In this context we develop the statements of the optimization problems based on guaranteed approach for the considered problems with incomplete information. For many realistic cases it is reasonable to use variants of the mini-max optimization, named as optimization for "the worst case scenario". Considered in this paper the structural optimization problems consist in finding of the shape and thickness distribution of axisymmetric quasi-brittle elastic shells with arising cracks in such a way that the cost functional (volume or weight of the shell material) reaches the minimum, while satisfying some constraints on the stress intensity factor and geometrical constraints. In the case of cycling loadings, we consider the number of loading cycles before fracture as the main constraint.

We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].