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International Applied Mechanics - 相似文献
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The functional in the principle of minimum potential energy of layered anisotropic shells with a nonlinear relationship between
strains and displacements is transformed into a canonical integral that coincides with the functional in the Reissner principle.
Partial forms of the functional are derived for problem formulations where the dimension can be reduced with respect to one
of the coordinates. The canonical system of equations is linearized and then normalized. The boundary-value problem is solved
by the numerical discrete-orthogonalization method. An anisotropic spherical shell under external compression is analyzed
for stability as an example 相似文献
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A. V. Boriseiko N. B. Zhukova N. P. Semenyuk V. M. Trach 《International Applied Mechanics》2010,46(3):269-278
A mixed variational principle is derived by Hamilton’s method from the principle of minimum potential energy for thin anisotropic
shells of revolution and is then used to derive a normal system of equations with complex coefficients. Discrete orthogonalization
is used to solve this homogeneous system and the nonlinear system of equations that describes the precritical state of shells.
A shell generated by revolving a circular arc around the axis parallel to its chord is analyzed for stability. The solution
is compared with the approximate solution obtained assuming that the precritical state is membrane. It is established that
the approximate problem formulation gives incorrect results for shells of negative Gaussian curvature 相似文献
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The equations for integral instantaneous characteristics of composite materials consisting of elastoplastic fibers and matrix are derived based on the known hypotheses of uniform strain or stress fields. The constitutive relations for a layered shell are obtained. The numerical algorithm elaborated is used to solve the stability problem for conical boron-aluminum shells under external pressure and axial compression. It is shown that the shells of medium thickness lose their stability under loads whose magnitude depends on the plasticity of the binder. The plasticity has a decisive influence on the choice of the optimum directions of reinforcement. If the parameters of a shell are such that the buckling occurs beyond the elastic limit, the shell must be reinforced in the direction of precritical stresses. However, this is possible only upon separate action of loads. 相似文献
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A study is made of the stability of boron-aluminum shells under a combination of axial compression and uniform external pressure.
An approximate theoretical model is constructed to describe the deformation of a layer of a fiber composite consisting of
elastoplastic components. The model is used to derive the equations of state of multilayered shells reinforced by different
schemes. The nonlinear equation describing the subcritical state is solved by the method of discrete orthogonalization with
the use of stepped loading. The homogeneous problem is also solved by discrete orthogonalization. It is shown that shells
can be efficiently designed for combination loading by plotting the envelope of the boundary curves for specific reinforcement
schemes. The envelope is convex for elastic shells and is of variable curvature for elastoplastic shells.
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya
Mekhanika, Vol. 35, No. 6, pp. 67–73, June, 1999. 相似文献
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