Analytic upper-bound estimates for the critical loads of perfect ribbed shells

A new approximate approach is proposed to find upper-bound estimates for the critical loads of ribbed shells. Seventeen cases are considered, and the minimum critical load parameter is determined __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 74–83, December 2005.     

Stability and load-bearing capacity of smooth and ribbed shells with local dents

A method for analysis of the stability and load-bearing capacity of imperfect smooth and ribbed shells is developed. This method is based on the finite-difference method and is implemented as an algorithm for fast calculation of critical forces, as opposed to the finite-element method. The theoretical results discussed include both early and recent results. The emphasis is on shells with local dents. The numerical results are successively corrected and compared with available experimental data for shells with a single dent and with other data. The method enables us to discover new features in the behavior of thin-walled structures under loading: development of precritical state, change in the dent shape, and exhaustion of load-bearing capacity. The lower local critical loads and upper stresses are determined. They correspond to general buckling and agree well with available experimental data.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 35–64, September 2004.     

Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

The paper proposes a method to calculate the natural frequencies of ribbed cylindrical shells with local axisymmetric deflections. The influence of initial imperfections of two types on the minimum frequencies of vibration is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 63–72, September 2008.     

On lower-bound estimates of critical loads for cylindrical shells

The paper proposes a new approach to estimate the lower bounds of critical loads for circular cylindrical shells. These bounds are compared with the ordinary lower bound of critical load under which a shell with initial deflections loses stability. The lower bound produced by the approach is higher than the ordinary bound and can be used in design __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 78–85, October 2006.     

Effect of localized imperfections on the critical loads of ribbed shells

A numerical approach to the assessment of the critical stresses for imperfect ribbed shells is developed. Initial deflections occupying a part of the shell surface (they are circumferentially bounded) are considered. The couple stresses and nonlinearity of the precritical state are taken into account. Numerical examples are given     

Stress function method in shakedown analysis of axisymmetric shells

A self-equilibrated stress obtained from the stress functions of thin shells is used for the static shakedown theorem as a residual stress. In combination with the finite element method, a linear programming formulation of the shakedown analysis of axisymmetric shells is derived. The physical meaning of the stress function method is clear and its computing amount is small. Some examples of the plates and shells show that the method is reasonable and efficient.The project was supported by the National Natural Science Foundation of China     

Analysis of axisymmetric phase strains in plates and shells

The axisymmetric strain problem for a shell in the direct phase transformation interval is formulated approximately as a nonlinear boundary-value thermoelastic problem with an implicit temperature dependence (through a phase parameter simulating the volume fraction of the new-phase crystals). The buckling problems for a circular plate and a shallow spherical dome of TiNi alloy loaded by normal pressure in the direct phase transformation interval are solved numerically. The branches of buckled equilibrium states are obtained for various values of the loading and phase parameters. It is found that the deflections increase abruptly with an increase in the phase parameter for a fixed value of the loading parameter. The evolution of the buckling modes and the phase-strain distribution along the meridian are studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 163–171, March–April, 2007.     

Solution of axisymmetric dynamic problems for cylindrical shells on an elastic foundation

A dynamic problem for a cylindrical shell on an elastic foundation is formulated. A numerical algorithm for solving this problem is outlined. The results obtained are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 103–109, December 2007.     

Solving axisymmetric dynamic problems for reinforced shells of revolution on an elastic foundation

The dynamic behavior of reinforced shells of revolution in an elastic medium is modeled. Pasternak’s model is used. A problem of vibration of discretely reinforced shells of revolution is formulated and a numerical algorithm is developed to solve it. Results from an analysis of the dynamic behavior of a reinforced spherical shell on an elastic foundation are presented as an example Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 99–106, February 2009.     

A note on the determination of critical loads for flexible noncircular cylindrical shells with clamped edges

An approach is proposed to determine the upper and lower bounds of the critical load for flexible noncircular long cylindrical shells with clamped longitudinal edges under nonuniform loading. An exact analytical solution is designed. Its critical points are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 78–87, November 2005.     

Effect of local loads on the stress-strain state of nonthin orthotropic conical shells

The paper analyzes the stress-strain state of nonthin orthotropic conical shells under local loads. The distribution of deflections and stresses in conical shells under local loads of some types is given as an example Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 103–113, August 2008.     

Analytical formulas of solutions of geometrically nonlinear equations of axisymmetric plates and shallow shells

Starting from the step-by-step iterative method, the analytical formulas of solutions of the geometrically nonlinear equations of the axisymmetric plates and shallow shells, have been obtained. The uniform convergence of the iterative method, is used to prove the convergence of the analytical formulas of the exact solutions of the equations.     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

Macroscopic strain potentials in nonlinear porous materials

By taking a hollow sphere as a representative volume element (RVE), the macroscopic strain potentials of porous materials with power-law incompressible matrix are studied in this paper. According to the principles of the minimum potential energy in nonlinear elasticity and the variational procedure, static admissible stress fields and kinematic admissible displacement fields are constructed, and hence the upper and the lower bounds of the macroscopic strain potential are obtained. The bounds given in the present paper differ so slightly that they both provide perfect approximations of the exact strain potential of the studied porous materials. It is also found that the upper bound proposed by previous authors is much higher than the present one, and the lower bounds given by Cocks is much lower. Moreover, the present calculation is also compared with the variational lower bound of Ponte Castañeda for statistically isotropic porous materials. Finally, the validity of the hollow spherical RVE for the studied nonlinear porous material is discussed by the difference between the present numerical results and the Cocks bound.     

不圆度对圆环和圆管静水压力下临界荷载的影响

采用最小二乘法求解曲率半径对称波动变化的非理想圆环在均匀静水压力作用下的平面内稳定性问题,分别求得了反对称屈曲和对称屈曲的临界荷载系数。当不圆度参数β=0．4时,反对称屈曲的临界荷载系数降低67．71％。用最小相对误差拟合法得到了精度较高的临界荷载系数拟合公式,其最大相对误差仅为土0．76％。采用平面应变假设,推广得到...     

Influence of orthotropy on displacements and stresses in nonthin cylindrical shells with elliptic cross section

An approach developed to solve boundary-value problems is used to analyze the influence of orthotropy and other factors on the displacement and stress fields in nonthin orthotropic cylindrical shells with elliptic cross-section __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 82–92, June 2007.     

Non-linear buckling behavior of FGM truncated conical shells subjected to axial load

In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the large deformation theory with von the Karman-Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis.     

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.     

Stability of axially compressed cylindrical shells made of reinforced materials with specific fiber orientation within each layer

A technique for stability analysis of anisotropic cylindrical shells is developed. It permits us to examine the cases of reinforcement where the elastic axes of layers do not coincide with the coordinate axes of the shell. The solution is obtained using the mixed equations of the Donnell-Mushtari-Vlasov theory of shells. The deflection and force functions are approximated by trigonometric series. Single-layer and multilayer cylindrical shells with fiber orientation of two types are analyzed for stability. It is revealed that when layers are few, failure to incorporate the direction of fibers in layers into the design model results in highly inaccurate values of critical loads __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 80–88, March 2006.