This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of weak shock waves. For solution of the problem it uses the integral and discrete Fourier transforms. Calculation of transformed dynamic stresses at the incisions of plates is held using the boundary-integral equation method and the theory of complex variable functions. The numerical implementation of the developed algorithm is based on the method of mechanical quadratures and collocation technique. For calculation of originals of the dynamic stresses it uses modified discrete Fourier transform. The algorithm is effective in the analysis of the dynamic stress state of defective plates.

Анотація: Якісний і достовірний розрахунок плит на пружних основах є одним із основних елементів проектування складних будівельних конструкцій. Існує надзвичайно велика кількість методів розрахунку, які не завжди досконалі і не дають чітких відповідей на важливі питання, що виникають у будівельній практиці. Ці питання стосуються як до проблеми вибору моделей пружних основ, так і розрахункових моделей оболонок і плит. Зокрема, у більшості випадків, використовувані у будівельних конструкці оболонки і плити є анізотропним, тому вибір їх розрахункових моделей таких елементів є надзвичайно важливим питанням. У статті розглядається осесиметрична задача згину нескінченної трансверсальноізотропної плити на пружній основі (пружному півпросторі), якою може бути плита дорожнього чи аеродромного покриттів під дією локальних навантажень. Визначаються контактні переміщення і напруження на поверхні розділу із врахуванням деформації поперечного зсуву і обтиснення.Ключові слова: пружні основи, контактні напруження і переміщення, трансверсальноізотропні плити, поперечний зсув і обтиснення, локальні навантаженя. Abstract:The qualitative and reliable calculation of plates on elastic bases is one of the main elements of the design of complex building constructions. There is an extremely large number of calculation methods, that are not always perfect. These mathods do not provide clear answers to important issues arising in building constructions. These questions relate to both problem. The first of this problem consists of the choosing models of elastic bases. The second problem consists of choosing of calculation models of shells and plates. In particular, in most cases, shells and plates, which are used in building structures, are anisotropic. So, the choice of their design models for such elements is an extremely important issue. The paper is aimed at the axisymmetric problem of bending an infinite transversal-isotropic plate on an elastic basis (elastic half-space), which can be the models of road slabs or airfield pavement, which are under the action of localized loads. On the basis of the equations of the generalized model of transversally isotropic plates, the solution of problem for the case of the plates on elastic bases is obtained. This solution corresponds to the case of the influence of localized loads. The contact displacements and stresses on the section surface are determined with accounting for the deformation of the transverse shear and compression. Obtained results coincide with the results of the classical theory of thin plates, when in the obtained equations are neglected by the listed refinements. The obtained results coincide with S. Lukasevych's results, when in the given formulas the members, which are corresponded transverse compression deformations, do not accoun for. Values of the contact displacements and pressures in the boundary of the plate and the elastic basis, which depend on the ratios of their modulus of elasticity, is summarized in the comparative table and the corresponding figures.

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The paper presents studies on the application of the boundary integral equation method for investigation of dynamic stress state of foam media with tunnel cavities in Cosserat continuum. For the solution of the non-stationary problem, the Fourier transform for time variable was used. The potential representations of Fourier transform displacements and microrotations are written. The fundamental functions of displacements and microrotations for the two-dimensional case of Cosserat continuum are built. Thus, the fundamental functions of displacement for the time-domain problem are derived as the functions of the two-dimensional isotropic continuum and the functions, which are responsible for the effect of shear-rotation deformations. The method of mechanical quadrature is applied for numerical calculations. Numerical example shows the comparison of distribution of dynamic stresses in the foam medium with the cavity under the action of impulse load accounting for the shear-rotation deformations effect and without accounting for this effect.

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