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  • 1
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, problems of bending of thin plates under the combined action of lateral loading and in-plane forces are studied by means of perturbation method.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The purpose of this paper is to introduce and to discuss several main variation principles in nonlinear theory of elasticity — namely the classic potential energy principle, complementary energy principle, and other two complementary energy principles (Levinson principle and Fraeijs de Veubeke principle) which are widely discussed in recent literatures. At the same time, the generalized variational principles are given also for all these principles. In this paper, systematic derivation and rigorous proof are given to these variational principles on the unified bases of principle of virtual work, and the intrinsic relations between these principles are also indicated. It is shown that, these principles have unified bases, and their differences are solely due to the adoption of different variables and Legendre tarnsformation. Thus, various variational principles constitute an organized totality in an unified frame. For those variational principles not discussed in this paper, the same frame can also be used, a diagram is given to illustrate the interrelationships between these principles.
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  • 3
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, an asymptotic elasto-plastic analysis in plane strain deformation near a crack tip is established. In this article, special emphasis is laid on the well-known Irwin's solution of elastic material. Thus, all the field quantity necessary for the elasto-plastic analysis of fracture mechanics can be obtained in this paper.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Applied mathematics and mechanics 1 (1980), S. 133-148 
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract After analysing the essential features of successive integration method taking displacement as variable by N. M. Newmark and E. L. Wilson et al, this paper presents a “Velocity” Element Method, taking velocity as variable for the solution of the initial value problem. A simplified scheme is offered for the non-damping system, and the stability is also discussed. Owing to the fact that this simplified scheme for non-damping and apparent static damping is explicit in form, it is unnecessary to solve the algebraic system of equations at every time interval, consequently the amount of computation is greatly reduced. For non-linear dynamic problems, this scheme may be used to obtain fairly good initial values for iteration. An extended form of “elocity” Element is presented for the arbitrary damping system. For the non-linear cases, the incremental Velocity iteration scheme is adopted and its convergence proved. Some discussions have been given on artificial damping and the effect of the parameter. Finally, the results of numerical calculatio of some typical problem are given in the appendix.
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  • 5
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Let the concentrated forces and the centers of pressure with unknown density functions x (ξ) and y (ξ) respectively be distributed along the axis z outside the solid, then one can reduce an axismmetric loading problem of solids of revolution to two simultaneous Fredholm integral equations. An iteration method for solving such equations is duscussed. A lemma equivalent to E. Rakotch's contractive mapping theorem and a theorem concerning the convergent proof of the iteration method are presented.
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  • 6
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the explicit forms of field functions in tetrehedron elements with 16 and 20 degrees of freedom are given in terms of volume coordinatesL 1,L 2,L 3,L 4 of tetrahedron.
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  • 7
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The scope of the present article, motivated by the case of the composite wooden propeller of an airplane, is to deal tentatively with the longitudinal free vibrationproblem of an elastic straight bar with a more general mathematical treatment. In this analysis, we have assigned to the modulus of elasticity, the bar cross section as well as the mass per unit length of the bar an exponential function variation, and then found a general solution, wherein three parameters were considered as the main factors to affect the longitudinal free vibration of the inhomogeneous elastic straight bar with a variable cross section.
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  • 8
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of the difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results.
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  • 9
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The purpose of this paper is to derive the equation of axisymmetrical ring shells with variable wall thickness in complex quantity and to give its general solution.
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  • 10
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation format is obtained. Its convergence is proved. We can get analytic expressions which converge to exact solution and its higher order derivatives unifornuy. Four numerical examples are given, which indicate that satisfactory results can be obtained by this method.
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