Аннотації
25.06.2018
Переміщення елементів зовнішніх несучих шарів в поперечному напрямку вважаються рівними нулю. Задачу зведено до системи диференційних рівнянь в частинних похідних відносно поздовжніх переміщень шарів, яку розв’язано за допомогою методу відокремлення змінних. Розв’язана модельна задача. Показано, що відсутність клею вздовж бічної сторони з’єднання може значною мірою збільшувати напруження біля краю клейового шару.
Перемещение элементов внешних несущих слоев в поперечном направлении считаются равными нулю. Задача сведена к системе дифференциальных уравнений в частных производных относительно продольных перемещений слоев, решение которой строится при помощи метода разделения переменных. Решена модельная задача. Показано, что отсутствие клея вдоль боковой стороны соединение может в значительной степени увеличивать напряжение у края клеевого слоя.
Here a simplified two-dimensional model of overlapping adhesive joint is proposed. The transverse displacements of the bearing layers are assumed to be zero. The stresses are assumed to be distributed uniformly over the thickness of the layers. The adhesive layer only works in shear, i.e. bending of the joint is absent. These simplifications make it possible to obtain an analytical solution of the problem. Here the stressed state problem of the adhesive joint of two variable thickness rectangular plates is solved, this joint has defects in the adhesive layer along the lateral sides. It is assumed that the joint has symmetry relative to the longitudinal axis. The problem is reduced to the second-order partial differential equations system relative to the longitudinal displacements of the outer bearing layers. The solution constructed by the variables separation method is an eigenfunctional series. The boundary conditions at the joint symmetry axis, at the lateral sides, at the edge of the glued area and bearing layers beyond of the adhesive layer (i.e., at the edge of the glued and not glued area) are exactly satisfied. The boundary conditions at the plates ends are satisfied by orthogonalizaiton of the residual to a system of eigenfunctions. The eigenfunctions are not orthogonal. The orthogonalization of the residual leads to a linear equations system relative to the unknown coefficients of the functional series. It is proved that the solution of the system can be obtained by the reduction method. The model problem is solved. Here is investigated the influence of the solution series terms number on the values of the coefficients entering into the solution. Mechanical effects are investigated, and it is shown that the defects in the adhesive layer can significantly increase the stresses at the edge of the adhesive layer. The comparison of the numerical results with the results obtained by finite element method is made. It is shown that the proposed approach to the problem has an accuracy, sufficient for the design problems.
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