Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

Natural vibration of a sandwich beam on an elastic foundation

The natural vibration of an elastic sandwich beam on an elastic foundation is studied. Bernoulli’s hypotheses are used to describe the kinematics of the face layers. The core layer is assumed to be stiff and compressible. The foundation reaction is described by Winkler’s model. The system of equilibrium equations is derived, and its exact solution for displacements is found. Numerical results are presented for a sandwich beam on an elastic foundation of low, medium, or high stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 57–63, May 2006.     

Thermoelastic bending of a sandwich plate on a deformable foundation

The thermoelastic bending of a circular light-core sandwich plate on a deformable foundation is examined. To describe the kinematics of the plate with asymmetric thickness, the hypothesis of broken normal is adopted. The reaction of the foundation is described by Winkler’s model. The thermomechanical load is local and symmetric. The system of equilibrium equations is derived and solved exactly. Numerical results for three-layer metal-polymer plate are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 96–103, February 2006.     

Extension of an elastic space with a rigid bar

An asymptotic model for deformation of an elastic space with a rigid thin reinforcing bar is constructed. The elastic modulus of the fiber far exceeds the elastic modulus of the matrix. The shape optimization problem for the reinforcing bar is solved on the basis of the uniform strength condition. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 120–128, January–February, 2008.     

Elastic-plastic deformation of sandwich rod on elastic basis

Sandwich composite material possesses advantages of both light weight and high strength. Although the mechanical behaviors of sandwich composite material with the influence of single external environment have been intensively studied, little work has been done in the study of mechanical property, in view of the nonlinear behavior of sandwich composites in the complicated external environments. In this paper, the problem about the bending of the three-layer elastic-plastic rod located on the elastic base, with a compressibly physical nonlinear core, has been studied. The mechanical response of the designed three-layer elements consisting of two bearing layers and a core has been examined. The complicated problem about curving of the three-layer rod located on the elastic base has been solved. The convergence of the proposed method of elastic solutions is examined to convince that the solution is acceptable. The calculated results indicate that the plasticity and physical nonlinearity of materials have a great influence on the deformation of the sandwich rod on the elastic basis.     

In-plane bending of a beam resting on a rigid rough foundation

Summary The bending of a finite-length beam that lies on a rigid, rough, flat foundation and interacts with it in accordance to the dry friction law is considered. Loading by bending moments applied at the ends of the beam is studied in detail. The problem is found to be a self-similar one. For small moments, the central part of the beam remains undeflected, and the problem reduces to the solution of an infinite system of algebraic equations. Large moments deflect the entire length of the beam, and the problem partly loses its self-similarity. In this case, the problem reduces to the solution of a successively decreasing number of ordinary differential equations along with some algebraical equations. The solution for the latter case provides initial conditions for the former one. This permits to obtain a solution for any value of the moment. Received 5 November 1996; accepted for publication 27 January 1997     

Buckling analysis of an elastic bar using the Bubnov-Galerkin method

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 148–156, January–February, 2008.     

Interaction of a die with a layered elastic foundation

Plane and axisymmetric contact problems for a three-layer elastic half-space are considered. The plane problem is reduced to a singular integral equation of the first kind whose approximate solution is obtained by a modified Multhopp-Kalandiya method of collocation. The axisymmetric problem is reduced to an integral Fredholm equation of the second kind whose approximate solution is obtained by a specially developed method of collocation over the nodes of the Legendre polynomial. An axisymmetric contact problem for an transversely isotropic layer completely adherent to an elastic isotropic half-space is also considered. Examples of calculating the characteristic integral quantities are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 165–175, May–June, 2006.     

Buckling and post-buckling of annular plates on an elastic foundation

On the basis of von Kárman equations,the axisymmetric buckling and post-bucklingof annular plates on anelastic foundation is(?)tematically discussed byusing shootingmethods.     

Analytical solution of cracked shell resting on elastic foundation

The elastostatic problem for cracked shallow spherical shell resting on linear elastic foundation is considered. The problem is formulated for a homogeneous isotropic material within the confines of a linearized shallow shell theory. By making use of integral transforms and asymptotic analysis, the problem is reduced to the solution of a pair of singular integral equations. The stress distribution obtained, around the crack tip, is similar to that of the elasticity solutions. The numerical results obtained agree well with those of previous work, where the elastic supports were neglected. The influences of the shell curvature and the modulus of subgrade reaction on the stress intensity factor are given.     

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.     

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.     

Analysis of bending, vibration and stability for thin plate on elastic foundation by the multivariable spline element method

I.IntroductionTheplatestructuresonelasticfoundationareofpracticalimportanceinwide-spreadapplicationsinengineering.Basedonrapidprogressofscienceandtechnologyaswellasengineeringconstructions,differentmodelsofeIasticfoundationaredeve1oped,sucha,Winkler,Vlazo…     

弹性地基上Euler-Bernoulli梁的热屈曲模态跃迁特性

采用解析方法研究了置于线性弹性地基上的Euler-Bernoulli梁在均匀升温载荷作用下的临界屈曲模态跃迁特性;分别在两端不可移简支和夹紧边界条件下,给出了弹性梁屈曲模态跃迁点的地基刚度值以及屈曲载荷值的精确表达式,并分析了模态跃迁特点.结果表明:随着地基刚度参数值的增大临界屈曲模态通过跃迁点从低阶次向高阶次跃迁;两端简支梁的模态跃迁具有突变特性,而两端夹紧梁的模态跃迁则是一个缓慢变化过程,它是通过端截面的弯矩或曲率的正负号改变实现的.     

Thermal impact on a circular sandwich plate on an elastic foundation

Symmetric transverse vibrations of a circular metal-polymer sandwich plate under a thermal impact are studied. The plate is connected with an inertialess Winkler foundation. The facesheets are assumed to satisfy the Kirchhoff hypothesis and the deformed normal in the low-density core is rectilinear and incompressible across thickness. Analytical solutions are obtained and their numerical analysis is given.     

General solution for dynamical problem of infinite beam on an elastic foundation

Based on the theory of Euler-Bernoulli beam and Winkler assumption for elasticfoundation,a mathematical model is presented.By using Fourier transformation for spacevariable,Laplace transformation for time variable and convolution theorem for theirinverse transformations,a general solution for dynamical problem of infinite beam on anelastic foundation is obtained.Finally,the cases of free vibration,impulsive response andmoving load are also discussed.     

Postbuckling behavior of an ideal bar on an elastic foundation

Novosibirsk. Translated from Prikladnaya Mekhanaika i Tekhnicheskaya Fizika, No. 2, pp. 130–142, March–April, 1994.     

Derivation of conditions of complete contact for a beam on a tensionless Winkler elastic foundation with Mathematica

The classical problem of a beam on a tensionless Winkler elastic foundation is reconsidered for the derivation of the conditions of complete contact between the beam and the foundation. This is achieved through the application of modern quantifier elimination software included in the computer algebra system Mathematica together with Taylor–Maclaurin series approximations to the deflection of the beam. Four particular beam problems have been considered in detail and the related QFFs (quantifier-free formulae) have been obtained for several values of the order in the series approximations. Additional approximation possibilities have also been investigated with an emphasis put on the use of the Galerkin method based on weighted residuals. The present results seem to constitute one more interesting application of modern quantifier elimination algorithms and the related software (here in Mathematica) to applied and engineering mechanics.     

CC series solution for bending of rectangular plates on elastic foundations

The analytical solution for the bending problem of the rectangular plates on an elastic foundation is investigated by using the Stockes' transformation of a double variables function. The numerical results for the rectangular plates with free edges on the elastic foundations under a concentrated force are given in the example. First Received Dec. 14 1993     

An approach to the contact problem for a circular punch on an elastic foundation

Rektorys’ approach is used in implementing the Ritz method to solve the contact problem for a circular punch on an elastic foundation of general form __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 65–71, April 2008.