Задачи механики сплошных сред со смешанными - Александров В.М.
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§ I. Method of orthogonal polynomials in the case of large values of X.
§ 2. Method of the reduction of equation (7.1) ch. I to an infinite system
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CONTENTS
of linear algebraic equations with a singular matrix of coefficients. Matrix regularization for small values of X. § 3. On the approximations of the kernel of integral equation (7.1) ch. I. Structure and properties of solutions of the integral equation for arbitrary values of X. Stability of solutions. § 4. Method of orthogonal polynomials, valid as small values of X. § 5. Exact solution of integral equation (7.1), (7.7) ch. I, in a form with singular integrals. The case of 2 intervals of integration and the periodic problem. Upper and lower bounds for an integral characteristic of a solution. § 6. A closed solution of integral equation (7.1), (7.7) ch. I, in a form without singular integrals. § 7. A method for establishing spectral relations of integral operators. § 8. Method of orthogonal functions, valid for all values of X. § 9. Direct methods for the solution of integral equation (7.1) ch. I. § 10. Problem of shim of an infinite elastic wedge.
Chapter 4. Methods for the solution of other mixed problems.
§ I. Asymptotic methods for solution of mixed problems of type b). § 2. -Reduction of the integral equation for the b) type problems to a linear algebraic system. § 3. Other versions of the b) type problems and the related metnods of solution. § 4. Integro-differential equations of Prandtl and Shtaermann. Principal methods of their solution. § 5. Reduction of the Prandtl and Shtaermann integro-differential equations on half-axis to difference equations with a shift. Methods for solution of difference equations. § 6. Asymptotic methods for solution of the c) type mixed problems. § 7. Other methods for solution of the c) type mixed problems. § 8. Contact problems taking into account friction forces. § 9. Contact problems with completely separated boundary conditions.
Chapter 5. Methods for solution of dynamical mixed problems.
§ I. Antiplane problem of vibrations of a stamp on an elastic half-space. § 2. Solution of a dynamical mixed problem of antiplane elastic layer deformation. § 3. Solution of dynamical mixed problems of antiplane flow in a layer of viscous liquid and of a strike of a body against an ideal liquid layer. § 4. Problems of the elasticity theory of describing a moving stamps. § 5. Problems of thin airfoil motion in a fluid. § 6. Supercavitation of an airfoil in an ideal liquid. § 7. Non-stationary problem of a ¦.compressible fluid (gas) flow from a reservoir.
Виктор Михайлович Александров,
Евгений Вениаминович Коваленко
ЗАДАЧИ МЕХАНИКИ СПЛОШНЫХ СРЕД CO СМЕШАННЫМИ ГРАНИЧНЫМИ УСЛОВИЯМИ
Редакторы: А. Г. Мордвинцев, В. А. Романов Художественный редактор Г. М. Коровина Технические редакторы В. Я. Кондакова,
Е. В. Морогова
Корректоры Г. В. Подволъская, Н. Д. Дорохова
HE № 12949
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