Conference publications

Abstracts

XXI conference

Mathematical model of stability of cylindrical shells

Yanovskaya E.A.

127055, RF, Moscow, Vadkovskiy, 3a

In the process of forming tubular billets distribution and crimpin continue oushigh degree of deformation loss of stability of the free part of the workpieceis not excluded in the form of buckling, in which the plastic statebilletis less stablethanelastic state.

Intensity hardening shell increases its stability, however, with increasing degree of deformation the intensity of hard eningand stability of the workpiece decrease. The theory of elasticity and plasticity are used to determine the parameters of tubeat the time of loss of stability. Basic differential equation of stability of a cylindrical shell under axial compression takes into account the forming shell. The stress and strain state of a cylindrical shell is approximately flat until moment of loss stability, so there are not stresses a cross the thickness and strain the medial surface. As a result of the see hypotheses and assumptions, we have alinear in homogeneous differential equation of the fourth order, which we solve using the Euler method. Characteristic equation is made by the form of the differential equation, the solution of which is the eigenvalues of the differential operator. In the next step constitutes a fundamental system of solutions of differential equations is made and the general solution of the differential equation is found. All the unknown constants are determined from the zero boundary conditions. In the loss of stability the shape of the curved surface of the shell is described by the resulting dependence. Condition bending the middle of the shell wall to find non-trivial solution is used. A system of linear equations is for finding the constants. This systemis solved by the Jordan–Gauss method. After substitution of the constants in the general solution, we have dependence describing the deflection of the middle surface of the shell. Results of analytical method are compared with the solution of the task of loss stability of cylindrical shells in the classical formulation for axisymmetric form of loss stability.

According to the obtained analytical dependences the model deflection of cylindrical shell allowed to analyze the behavior of workpieces with different initial height at a fixed relative wall thickness. This mathematical model does not conflict with known theoretical theories and experimental datas.

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