Calculation of the stability of composite rods according to the non-classical bending model

The problem of the effect of deformations of transverse shear and transverse compression on the value of the critical stress in the problem of the loss of stability of a transversely isotropic rod is considered. The fourth-order differential equation of the nonclassical bending model of rods is applied. Formulas for the critical stress are obtained, as well as numerical results for rods made of different material

The Problem of the Reliability of Bending Models for Composite Plates of Medium Thickness

Most refined bending models of medium-thick plates, which consider transverse shear and partial compression deformations, differ little. However, despite a significant increase in the order of the governing differential equations, the results obtained from their equations give mainly a small increase in accuracy compared to the existing theories. On the other hand, such an increase in the order of the constructed systems of differential equations requires a significant increase in the effort required to solve them, complicates their physical interpretation, and narrows the range of people who can use them, primarily engineers and designers. Therefore, developing a plate-bending model that incorporates all the above factors and is on par with previously applied theories regarding the complexity of the calculation equations remains relevant. For example, most of the applied theories that do not consider transverse compression cannot be used to solve problems of contact interaction with rigid and elastic dies and bases because it is impossible to satisfy the conditions at the contact boundary of the outer surface of the plate, as well as the boundary conditions at the edges of the plate. Therefore, to provide guaranteed accuracy of the results, some researchers of these problems have introduced such a concept as “energy consistency” between the functions of representation of the displacement vector components, their number, the order of equations, and the number of boundary conditions. The authors, based on the developed version of the model of orthotropic plates of medium thickness, investigate the problem of taking into account the so-called “energy consistency” effect of the bending model, depending on the order of the design equations and the number of boundary conditions, as well as its usefulness and disadvantages in practical calculations. The equations of equilibrium in displacements and expressions for stresses in terms of force and moment forces are recorded. For rectangular and circular plates of medium thickness, test problems are solved, and the numerical data are compared with those obtained using spatial problems of elasticity theory, as well as the refined Timoshenko and Reissner theories. An analysis of the obtained results is provided

Dynamic stress concentration at the boundary of an incision at the plate under the action of weak shock waves

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

Bending of Orthotropic Plate Containing a Crack Parallel to the Median Plane

This paper considers cylindrical bending of the plate containing a crack parallel to plate's faces. The analytical model of the problem is obtained using the improved theory of plates bending, which considers transverse deformation of the plate. Received analytical results are compared with the numerical data of the boundary element approach, which is modified to suit the considered contact problem. The results of analytical and numerical techniques are in a good agreement both for the isotropic and anisotropic plates

Stress state of plate with incisions under the action of oscillating concentrated forces

This paper proposes the novel technique for analysis of dynamic stress state of multi-connected infinite plates under the action of oscillating forces. Calculation of 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 algorithmis based on the method of mechanical quadratures and collocation technique. The algorithm is effective in the analysis of the stress state caused by steady-state vibrations of plates

Contact problem for plate with triangular hole and system of two rigid punches with corner points

Побудовано систему двох сингулярних інтегральних рівнянь з логарифмічними ядрами в задачі про тиск на контур трикутного отвору в нескінченній пластинці системи двох штампів з кутовими точками. Методом граничної колокації досліджується вплив на напружений стан пластинки форми отвору і величини зони контакту.The system of two singular integral equations with logarithmic kernel in the problem about pressure on the contour triangular hole in the infinite plate by the system of two punches with corner points is built. The effect of the form of hole and the value of contact zone on the stress state of plate by boundary collocation method is investigated