Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.     

Stress-strain analysis of a composite truncated conical shell

The stress-strain state of a nonshallow truncated conical shell made of a composite material and subjected to axial forces at the ends is studied. A variational difference method is used. Calculations are carried out for an orthotropic shell with low shear stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 66–72, July 2007.     

边界元法分析薄形层合结构

薄形层合结构由于几何形状的特殊性,其力学分析是数值计算的难点.边界元法分析层合结构具有较大的优势,但对于薄形层合结构,边界源点和对边上的积分单元距离很近,边界积分方程中存在几乎奇异积分,常规的数值积分方法已经失效.文章引入一种半解析化方法,计算薄形层合结构边界元法中的几乎奇异积分,使边界元法能成功分析三维薄形层合结构的层间界面应力和各层内点力学参量.     

Thermoconductivity and thermoelasticity of thin isotropic shells heated by a moving heat pulse

The paper presents a solution to the problem of thermal conduction and thermoelasticity for a thin shallow spherical shell heated by a concentrated or local impulsive heat source moving over the shell surface. It is assumed that temperature is linearly distributed across the shell thickness and that the shell, on its sides, exchanges heat with the environment in accordance with Newton’s law of cooling. The Fourier and Laplace transforms are used to find an analytic solution. The dependence of the temperature field and stress/strain components on the type of heating and the form of heat source is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 85–92, November 2006.     

Scaled-boundary method in electroelasticity of thin plates

The paper discusses the scaled-boundary method as applied to electroelastic problems. As an example, the stress-intensity factor is calculated for a thin rectangular piezoelectric plate with an edge crack __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 124–134, July 2006.     

Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.The English text was polished by Yunming Chen.     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

AN EXACT METHOD OF BENDING OF ELASTIC THIN PLATES WITH ARBITRARY SHAPE

ＡＮ　ＥＸＡＣＴ　ＭＥＴＨＯＤ　ＯＦ　ＢＥＮＤＩＮＧ　ＯＦ　ＥＬＡＳＴＩＣ　ＴＨＩＮ　ＰＬＡＴＥＳ　ＷＩＴＨ　ＡＲＢＩＴＲＡＲＹ　ＳＨＡＰＥＺｈｏｕＤｉｎｇ（周叮）（ＲｅｃｅｉｖｅｄＡｐｒｉｌ１０，１９９５，ＲｅｖｉｓｅｄＡｐｒｉｌ２６．１９９６．Ｃ...     

Nonlinear static and dynamic analysis for laminated,annular, spherical caps of moderate thickness

Based on Timoshenko-Mindlin kinematic hypothesis, the shallow shell theory is extended to include the transverse shear deformation for the nonlinear axisymmetric dynamic analysis of the symmetric cross-ply shallow spherical shell. Using the orthogonal point collocation method and the Newmark scheme, an iterative solution is formulated. The numerical results for the nonlinear static and dynamic responses and dynamic buckling of these shallow spherical shells with circular holes under uniformly distributed static or dynamic normal impact loads are presented and compared with available data.     

任意叠层球壳内的应力波传播

提出一种有效求解方法，求解了任意叠层球壳在动载荷作用下的应力波传播。首先，利用有限Ｈａｎｋｅｌ变换和Ｌａｐｌａｃｅ变换求解了每一单层的弹性动力学解。然后，利用叠层球壳的内、外边界条件和层与层之间的连接条件确定每一单层解中的待定常数。从而，我们可以得到应力波在叠层球壳内传播的精确解。最后，我们计算了在一个突加内压作用下的两层球壳（Ｓｔｅｅｌ／Ａｌ）和三层球壳（Ｓｔｅｅｌ／Ａｌｌｏｙ／Ａｌ）内的应力波传播。求解过程和计算结果表明文中提出的求解方法是简便可行的。