Моделювання клейового з’єднання деталей з різними пружними характеристиками

Abstract

Пропонується спосіб визначення ширини зони контакту гладкої смуги, що притискається до абсолютно жорсткої півплощини нормальним зосередженим навантаженням. Отримано сингулярне інтегральне рівняння задачі, розв’язок якого знайдено методом механічних квадратур. Частково проаналізовано вплив товщини та пружних характеристик смуги наширину зони контакту. The author suggests to model the adhesive joint of two parts by means of elastic linkages. If one part is substantially more rigid than the other, while the contact region is almost flat, such structure can be modelled via the problem of one-side contact of an elastic plate with absolutely rigid half-plane. Plane deformation of a uniform isotropic smooth band pressed to absolutely rigid half-plane with the normal fixed load is considered. There is an elastic contact between the band and the half-plane: it is assumed that normal shifts in the contact region are null, while outside the contact region normal shifts of band’s lower edge points are proportional to normal loads in the points of this edge. To solve the problem, a new function of type (8) is introduced and the singular integral equation with logarithmic singularity is built under this function. The equation is reduced to the singular integral equation with Cauchy type kernel where there is additional condition. As there is no angular point in the lower edge form of a band deformed by the normal fixed pressing load, normal strains near contact region boundaries have singularity of the same type as in the contact problem of a band deformed by the stamp without angular points; this encourages seeking the solution of the equation in form of a function with root property. Mechanical quadrature method is used for solution of this equation. Conditions (5) are used to define the width of contact region. Numerical experiments result in the following conclusions: there is linear dependence of contact region width on the thickness of the band and shift module if the values of elastic linkage coefficients are fixed; increase of band’s thickness causes increase of contact region width; increase of shift module causes decrease of contact region width. The performed numerical experiments agree with what is said in [3] and are not at variance with physical meaning.