Olesia Maksymovych

A method for selecting the optimal shape of holes, taking into account the strength anisotropy of composites, is proposed. The methodology includes the following: an algorithm for stress determination based on singular integral equations and Green’s solutions; a strength criterion for the boundary of unloaded holes, which takes into account the anisotropic mechanical and strength properties of composites; an algorithm for determining hole shapes by a formulated nonlinear programming problem. The results of the research are presented for holes of various shapes, including single- and double-periodic hole systems. It is established that the calculated allowable loads for composite plates with holes based on stress concentration factors can be significantly overestimated. At the same time, by designing holes of optimal shape, the allowable loads can be many times greater than those for circular holes.

A method for selecting mechanical properties and geometry of reinforcing overlays to increase the strength of composite structural elements with holes has been developed. The method is based on the developed algorithm for calculating stress concentration near holes reinforced with inserted rings or glued composite reinforcing overlays. The determination of stresses near holes and overlays is reduced to solving a system of singular integral equations. The kernels of these equations are constructed using Green’s solution, which allows a reduction in the number of equations to four. It is shown that the stress concentration near holes can be significantly reduced by optimizing the thickness, elastic properties, and shape of the overlays. The stress calculations performed based on the three-dimensional theory of elasticity confirmed the reliability of the results obtained within the framework of the plane problem of an anisotropic body. The results obtained, in accordance with the concept of sustainable development, enable the develop simple methods for increasing reliability, reducing material consumption, and reducing the manufacturing and operating costs of composite structures in the aerospace and mechanical engineering industries.

A novel approach to the calculation and optimization methodology of repairable elements of unmanned aerial vehicle (UAV) structures using pre-cured composite patches is proposed. These patches are glued to the damaged structure with adhesives filled with short fibers or particulate fillers. Compared with conventional repair procedures (in which composite prepregs or wet lay-up are used), the suggested method allows damaged UAV structures to be repaired relatively quickly in field conditions without the need for a vacuum or special equipment. In most scientific studies on this problem, significant attention is devoted to the investigation of rectangular patches used for reinforcing plates that have defects such as cracks and damage. This study focuses on the potential application of circular patches for reinforcing plates with defects or damage and includes further parametric optimization of the geometric parameters of the patch. A fundamental approach to the topological and structural optimization of adhesive bonding, along with an experimental study of adhesive properties, has been combined into a single model. This model includes the optimization of the shape and structure of patches for bonded repair, allowing for changes in adhesive thickness to restore the load-carrying capacity of the structure. The simulation and analysis of the results of the renovation of damaged structures for double-sided and single-sided repaired elements of the UAV structure were performed.

The elasticity problem of an anisotropic body with cracks under the action of time-varying loads and harmonic waves is studied at the antiplane dynamic consideration. To solve the problem, the basic equations are reduced to the consideration of dynamic problems for some isotropic material. The obtained equations were solved using the Laplace integral transformation. Laplace transforms are found on the basis of the method of integral equations and are reduced to solving hypersingular integral equations. A numerical method for solving the obtained equations using the quadrature method is proposed. The Laplace inversion is performed numerically on the basis of pre-regularized formulas that allow the calculation of stresses with controlled accuracy. A study of the stress concentration near cracks under dynamic loads and falling waves was performed.