Dynamical problem for an incompressible laminated cylinder with helical anisotropy. Part 2. Numerical analysis

For weakly compressible elastic helically orthotropic laminated cylinders loaded by internal impulsive pressure under conditions of plane deformation, we perform the numerical investigation of the character of convergence of one-dimensional wave solutions to the analytic relations for incompressible thick-walled shells obtained earlier by the author. An approximate engineering analytic procedure is proposed for the evaluation of the dynamic stress-strain state of inhomogeneous helically reinforced thick-walled cylindrical shells. __________ Translated from Problemy Prochnosti, No. 1, pp. 114–120, January–February, 2007. Notation is taken from Part 1 of the present work [1]. Here, we continue the numeration of formulas started in Part 1 and the reader is frequently referred to the formulas presented there.     

Singularities of the Solution of the Dynamic Problems of the Elasticity Theory for Metal Composite Cylinders Near Free Ends

Strength of Materials - The singularities of the solution of the dynamic problems of elasticity theory in the vicinity of the normal section (at a right angle) of the perfect contact surface...     

Stability of properties of Kolmogorov complexity under relativization

Assume that a tuple of binary strings \(\bar a\) = 〈a ₁ ..., a _n 〉 has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of \(\bar a\) do not change significantly if we relativize them to b? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an ?-formula). In particular, we show that a random (conditional on \(\bar a\)) oracle b does not help to extract common information from the strings a _i .     

Modeling of Three-Dimensional Stress-Strain State and Strength Analysis of Metal Composite Cylinders under Impulsive Loading Using the Conwep Method

Strength of Materials - The application package previously developed at the Pisarenko Institute of Problems of Strength of the National Academy of Sciences of Ukraine for the numerical calculation...     

Numerical studies on the dynamic behavior of multilayer thick-walled cylinders with helical orthotropy

The Wilkins two-dimensional algorithm-based method of numerical studies on the dynamic behavior of multilayer thick-walled cylindrical shells with different spiral reinforcement structures is developed. Test calculations are in good agreement with known solutions. The dynamic behavior of a two-layer cylinder with different spiral reinforcement structures is investigated.Translated from Problemy Prochnosti, No. 6, pp. 99–110, November–December, 2004     

Method of investigating the nonaxisymmetric dynamic form changing of collapsible shells. Report 2. Calculations and experiment

The theory and numerical method of calculating the significant nonstationary form change of nonaxisymmetric elastoplastic shells with allowance for material failure are confirmed. The confirmation is based on numerical experimentation, and comparison of numerical results with test calculations and experimental data. Satisfactory accuracy is noted for this numerical method and the computational results obtained. Some characteristic features of the dynamic failure of the shells are disclosed.Translated from Problemy Prochnosti, No. 4, pp. 41–48, April, 1996.     

Method of investigating nonaxisymmetric dynamic form change in failing shells. Report 1. Theory and numerical method

A mathematical theory describing processes of vigorous dynamic form change in elastoplastic nonaxisymmetric shells is proposed. The damage sustained by the material right up to failure is considered. An analytical method of calculating the nonstationary load on a shell is presented for the case of a hydrodynamic loading. A numerical integrointerpolation method of solving the indicated initially boundary nonlinear nonstationary problem is developed.Translated from Problemy Prochnosti, No. 3, pp. 5–19, March, 1996.     

A method of solving three-dimensonal nonstationary problems of hydroelasticity with allowance for fluid failure

A numerical-analytical method of solving one class of nonlinear problems of dynamic hydroelasticity is proposed. The essence of the method consists in the expansion of all unknowns in trigonometric Fourier series in terms of the angular coordinate with subsequent application of the finite-element method over a two-dimensional grid. As a rule, it has been used to date to solve linear problems. Good accuracy of the developed algorithm is demonstrated on the basis of numeric experiments and trial calculations, and several specific examples are solved. A number of effects associated with the different behavior of an ideally elastic and rupturable fluid are observed.Translated from Problemy Prochnosti, No. 5, pp. 79–83, May, 1991.