Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

Stress state of a cylindrical composite panel weakened by a circular hole

The paper studies the stress-strain state of a deep cylindrical panel weakened by a hole and subjected to a tensile load at the outer boundary. A variational difference method is used. A numerical analysis is carried out for an orthotropic panel with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 73–78, May 2006.     

Nonlinear deformation of a particulate material in complex stress state

An algorithm is proposed to determine the effective deformation properties and stress-strain state of particulate composite materials with physically nonlinear components and complex stress state. The laws that govern the deformation of particulate composites are studied. A particulate composite is considered a two-component material of random structure. Its effective properties are determined by conditional averaging. The nonlinear equations that incorporate the physical nonlinearity of the components are solved by the method of successive approximations. The relationship between macrostresses and macrostrains is established. The effective deformation properties of a particulate composite as a function of the volume fractions of the components and stress state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 50–60, March 2006.     

Axisymmetric thermoelastoplastic stress-strain state of flexible laminated transversely isotropic shells

The paper presents a technique for numerical analysis of the elastoplastic stress-strain state of flexible laminated shells of revolution made of isotropic and transversely isotropic materials and subjected to axisymmetric loading and heating. The technique is based on the Kirchhoff-Love hypotheses for the whole laminate. The deformation of the isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of the transversely isotropic material is described using the flow theory with isotropic hardening. The process of loading is divided into steps at each of which the stress-strain state is determined by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 76–86, December, 2006.     

The stress-strain state of a plate with a multilayer inclusion

A modified boundary-element method is proposed to analyze the stress-strain state of a plate with a multilayer inclusion of arbitrary shape. The two-dimensional approximation of displacements on each boundary element makes it possible to determine all the stress/strain components at the interface between the inclusion and each layer. The stress state of a plate with an elliptical and a rectangular multilayer inclusion under unidirectional tension (a load uniformly distributed along the edges) is analyzed as numerical examples. The numerical examples demonstrate high accuracy and computational efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 104–110, March 2007. For the centenary of the birth of G. N. Savin.     

Refined analysis of the stress state of orthotropic elliptic cylindrical shells with variable geometrical parameters

An approach developed earlier to solve boundary-value problems is used to analyze the behavior of the stress-strain state of orthotropic elliptic cylindrical shells with variation in the geometric parameters of their cross section at constant volume (weight) Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 53–62, September 2008.     

Stress-strain state and durability of mechanically inhomogeneous welds under low-cycle loading

Relations are proposed for the determination of the stress-strain state, strength, and life of butt welds with mild and hard interlayers under cyclic elastoplastic tension-compression. The accumulation of cyclic and quasistatic damages is determined with allowance for the redistribution of the cyclic elastoplastic strains and hardness of the stress state due to changes in the cyclic properties of separate regions of welds. The theoretical distribution of cyclic strains and the durability of welds under cyclic elastoplastic loading are supported by experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 29–38, February 2008.     

Microdamage of a nonlinear elastic material in combined stress state

The structural theory of short-term damage is used to study the coupled processes of deformation and microdamage of a physically nonlinear material in a combined stress state. The basis for the analysis is the stochastic elasticity equations for a physically nonlinear porous medium. Damage in a microvolume of the material is assumed to occur in accordance with the Huber-Mises failure criterion. The balance equation for damaged microvolumes is derived and added to the macrostress-macrostrain relations to produce a closed-form system of equations. It describes the coupled processes of nonlinear deformation and microdamage of the porous material. Algorithms are developed for calculating the dependence of microdamage on macrostresses and macrostrains and plotting stress-strain curves for a homogeneous material under either biaxial normal loading or combined normal and tangential loading. The plots are analyzed depending on the type of stress state __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 30–39, November 2006.     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

Stress-strain solutions for circumferentially corrugated elliptic cylindrical shells

The paper presents an approach to solve the boundary-value stress-strain problem for circumferentially corrugated elliptic cylindrical shells. The approach employs splines to approximate the solution and the stable discrete-orthogonalization method to solve the resulting one-dimensional problem. The results are presented as plots and a table __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 70–78, September 2006.     

Elastoplastic Axisymmetric Stress-Strain State of Laminated Shells Made of Isotropic and Transversely Isotropic Materials with Different Moduli

A method is developed for analysis of the elastoplastic stress-strain state of laminated shells of revolution under axisymmetric loading. The shells are made of isotropic and transversally isotropic materials with different moduli. The method is based on the Kirchhoff-Love hypotheses for the whole laminate, the theory of deformation along paths of small curvature (for isotropic materials), and the theory of elasticity with different tensile and compressive moduli (transversely isotropic materials). The problem is solved by the method of successive approximations. Numerical examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 88–96, August 2005.     

Mesomechanics of deformation and short-term damage of linear elastic homogeneous and composite materials

The structural theory of microdamage of homogeneous and composite materials is generalized. The theory is based on the equations and methods of the mechanics of microinhomogeneous bodies with stochastic structure. A single microdamage is modeled by a quasispherical pore empty or filled with particles of a damaged material. The accumulation of microdamages under increasing loading is modeled as increasing porosity. The damage within a single microvolume is governed by the Huber-Mises or Schleicher-Nadai failure criterion. The ultimate strength is assumed to be a random function of coordinates with power-law or Weibull one-point distribution. The stress-strain state and effective elastic properties of a composite with microdamaged components are determined using the stochastic equations of elasticity. The equations of deformation and microdamage and the porosity balance equation constitute a closed-form system of equations. The solution is found iteratively using conditional moments. The effect of temperature on the coupled processes of deformation and microdamage is taken into account. Algorithms for plotting the dependences of microdamage and macrostresses on macrostrains for composites of different structure are developed. The effect of temperature and strength of damaged material on the stress-strain and microdamage curves is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 3–42, June 2007.     

Numerical-Analytic Solution of Boundary-Value Stress-Strain Problems for Rotating Anisotropic Cylinders

A numerical-analytical approach is proposed to solve boundary-value stress-strain problems for hollow inhomogeneous cylinders under centrifugal loading. Their elastic characteristics vary in both radial and circumferential directions. The governing system of ordinary differential equations is derived using Fourier series for stresses and displacements. It is solved by the discrete-orthogonalization method. Solutions to specific problems are exemplified __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 82–87, August 2005.     

Elastoplastic stress-strain state of flexible layered shells made of isotropic and transversely isotropic materials with different moduli and subjected to axisymmetric loading

The paper proposes a numerical technique for analysis of the elastoplastic stress-strain state of flexible layered shells of revolution under axisymmetric loading. It is assumed that the shells are made of isotropic and transversely isotropic materials with different moduli in tension and compression. The technique is based on a geometrically nonlinear theory of shells that takes into account the squared angles of rotation and the Kirchhoff-Love hypotheses for a layer stack. The deformation of isotropic materials is described using the theory of deformation along paths of small curvature. The deformation of transversely isotropic materials is described using the theory of elasticity with different moduli in tension and compression. The problem is solved by the method of successive approximations. A numerical example is given __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 31–42, November 2007.     

MEASUREMENT IN TENSILE TEST OF TRUE STRESS-STRAIN CURVES FOR LOW-CARBON STEEL1)

针对低碳钢拉伸的真应力-应变曲线测量问题,开发了基于单相机三维数字图像相关的实验教学系统。该系统可测量低碳钢拉伸过程中的表面三维形貌和表面应变,并由此获得低碳钢拉伸的真应力-应变曲线。该实验有助于学生深入理解塑性金属材料的力学性能,培养其科研兴趣。     

Rock deformation problems

Studies into the stress-strain state of rock mass are reviewed. The solutions of a wide range of applied problems are analyzed and methods used to solve them are generalized. Important areas of further research in rock mechanics are pointed out.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 3–17, December 2004.     

High-strain-rate compressive behavior of a rigid polyurethane foam with various densities

The dynamic compressive stress-strain behavior of a rigid polyurethane foam with four values of density (78, 154, 299, and 445 kg/m³) has been determined in the strain-rate range of 1000–5000 s⁻¹. A pulse shaping technique was used with a split Hopkinson pressure bar to ensure homogeneous deformation in the foam specimens under dynamic compression. Dynamic stress equilibrium in the specimen was monitored during each experiment using piezoelectric force transducers mounted close to the specimen end-faces. Quasi-static experiments were also performed to demonstrate rate effects. Experimental results show that both the quasistatic and the dynamic stress-strain curves of the foam exhibit linear elasticity at small strains until a peak is reached. After the peak, the stress-strain curves have a plateau region followed by a densification region. The peak stress is strain-rate sensitive and depends on the square of the foam density.     

Deformation and fracture resistance of butt-welded joints with mild interlayer under elastoplastic tension

Relations are proposed for evaluating the stress-strain state and strength of a butt weld with a mild interlayer under elastoplastic tension in plane-and axisymmetric-strain conditions. The relations allow for the distribution of transverse normal stresses across the interlayer thickness and the interaction and hardening of the metals in the elastoplastic domain. The predicted strain distribution in certain areas of the weld and its strength are verified experimentally __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 119–127, April 2006.     

Photovisco-elasto-plastic analysis tested on polyester by the scattered-light method

A three-dimensional photovisco-elasto-plastic model considering the strain rate effect was investigated by the scattered-light method using polyester as a model material. To examine the mechanical and optical properties of the material, tension and torsion tests were carried out on cylindrical specimens under various strain rates at 30°C. The effects of strain rate on the stress-strain relation and scattered-light fringe appearance were evaluated. The equivalent shearing stress-strain relation can be approximated by the Ramberg-Osgood equation with rate-dependent modulus and yield stress. The fringe gradient, when normalized by a rate-dependent yield gradient, can be related to an equivalent strain in the same form regardless of the strain rate. The strain rate can be evaluated from the measurement of the rate of increase of the fringe gradient. Hence, the relation between the fringe gradient and its rate of increase was derived as a function of strain rate. Finally, a method is proposed for the estimation of the visco-elasto-plastic stress and strain in a three-dimensional specimen from the measurement of only the fringe gradient and its rate of increase. The method was successfully applied not only to uniaxial tension but also to pure torsion.     

Solution of contact problems on the basis of a refined theory of plates and shells

Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008.