Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson’s ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions.
The present study consists of two parts. The first part supplies an exact semi-analytical solution for a general model of rigid plastic strain hardening material at large strains. The second part applies this solution to tube hydroforming design. The solution provides stress and velocity fields in a hollow cylinder subject to simultaneous expansion and elongation/contraction. No restriction is imposed on the hardening law. A numerical method is only required to evaluate ordinary integrals. The solution is facilitated using Lagrangian coordinates. The second part of the paper is regarded as an alternative to the finite element design of tube hydroforming processes, restricted to rather simple final shapes. An advantage of this approach is that the hardening law is not required for calculating many process parameters. Therefore, the corresponding design is universally valid for all strain hardening materials if these parameters are of concern. In particular, the prediction of fracture initiation at the outer surface is independent of the hardening law for widely used ductile fracture criteria. The inner pressure is the only essential process parameter whose value is controlled by the hardening law.
The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.
Seismic analysis still has many issues to be investigated not only in countries which are situated in seismic regions but also in European countries, as it was seen in Italy, Greece and Turkey in 2017 [1]. Based on calculations, methods of theoretical and experimental research we performed synthesis reactions of the structural systems of the console type on the seismic effects. To identify structural architectonics of objects, a regular structure which includes geometrically non‐changeable (or slightly changeable) vertical spinal fragments and seismic safety bearing members with plastic hinges at the nodal connections is used. The determining factor of the stress‐strain state of the structural system is the angular displacement relative to the base in the form of deviations close to the rectilinear approximation. The method of seismic analysis of inelastic cantilever column systems of regular structure is developed [2]. The method is based on the energy principle for analysis of inelastic systems as a quasistatic problem. The results can be extended for ecological materials such as bamboo [3].
The main criterion for the performance of welds is the strength. The least durable are the corner joints used to perform various types of welded joints. In the literature, the methods of calculating the strength of welded joints with solid seams are considered in sufficient detail. Methods of calculation of connection interrupted sutures absent. In this case, the greatest difficulty is the calculation of connections using circular intermittent seams, which are often performed in welded drums and pulleys. They work on torsion. Therefore, the development of methods for calculating circular intermittent seams for torsion is quite important. Shear stresses in welds from torque are determined depending on the value of the polar moment of resistance of its dangerous section. When determining the polar moment of resistance of the dangerous section of a circular discontinuous seam, it was represented by a set of sections in the form of a sector of a circular ring. The method of calculation of the polar moment of resistance of the rotated dangerous section of a circular discontinuous weld, which takes into account the relative length of the weld areas and their number, is proposed, as well as the method of accurate and approximate calculation of shear stresses in the weld.
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