On some constitutive equations for micropolar plates

ChrÃ3sÌcielewski, J.; Witkowski, Wojciech

doi:10.1002/zamm.200900366

Cited by 19 publications

(22 citation statements)

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“…Since the role of a t was not understood within the general sixfield theory of elastic shells, Chróścielewski et al (2004) and Chróścielewski and Witkowski (2010a) performed extensive numerical tests in order to analyse how values of a t influence the static and dynamic behaviour of several regular and irregular elastic shell structures within the linear and geometrically non-linear range of deformation. It was found, in particular, that when a t < 1 the results were practically insensitive to its numerical value.…”

Section: Discussionmentioning

confidence: 99%

“…Altenbach and Eremeyev (2009) suggested that the constitutive relations used in the general shell theory may be viewed as equivalent to their material law proposed for the Cosserat plates. In particular, Chróścielewski and Witkowski (2010a) derived from results of Altenbach and Eremeyev (2009) the analytic formula for a t valid in the case of non-polar material:…”

Section: ð1:23þmentioning

confidence: 99%

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On shear correction factors in the non-linear theory of elastic shells

Chróścielewski

Pietraszkiewicz

Witkowski

2010

International Journal of Solids and Structures

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a b s t r a c tTheoretical values of two correction factors a s = 5/6 and a t = 7/10 are established for the respective transverse shear stress resultants and stress couples within the general, dynamically and kinematically exact, six-field theory of elastic shells. These values do not depend on the shell material symmetry, geometry of the base surface, the shell thickness, or any kind of kinematic and/or dynamic constraints. The analysis is based on the complementary energy density following from the transverse shear stresses acting only on the shell cross section. The appropriate quadratic and cubic distributions of the stresses across the thickness allow one to derive the consistent constitutive equations for the transverse shear stress resultants and stress couples with a s and a t as the respective correction factors. Four numerical examples of highly non-linear shell structures illustrate the influence of different values of a s and a t on the results. In particular, some influence of a t is noticed on the placement of bifurcation points. In dynamic problem of flight of three intersecting plates analysed with Newmark-type temporal algorithm, the value of a t influences the moment at which the relative error of total energy of the system begins to grow indefinitely leading to the solution failure.

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Section: Discussionmentioning

confidence: 99%

Section: ð1:23þmentioning

confidence: 99%

On shear correction factors in the non-linear theory of elastic shells

Chróścielewski

Pietraszkiewicz

Witkowski

2010

International Journal of Solids and Structures

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“…The boundary-value problem (6), (7), (15), and (16) supplemented by the constitutive equation (17) describes finite deformations of the isotropic micropolar shell. Numerical solutions of few examples are presented in [16][17][18][19] among others.…”

Section: Dynamics and Statics Of Micropolar Plates And Shellsmentioning

confidence: 99%

On the Variational Analysis of Vibrations of Prestressed Six-Parameter Shells

Altenbach

Eremeyev

2016

Computational Modeling, Optimization and Manufacturing Simulation of Advanced Engineering Materials

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We discuss the variational statements of the theory of linear vibrations of prestressed six-parameter shells. Initial or residual stresses can significantly influence buckling and oscillations of thin-walled structures. Within the six-parameter theory of shells a shell is modeled as a deformed material each point of it has six degrees f freedom, that is three translational and three rotational ones. Starting with the governing equations of the six-parameter shell theory the constitutive equations are analyzed. The linearization of the boundary-value problem is realized. After a brief discussion of the eigen-vibrations of the prestressed six-parameter shells the Rayleigh principle is introduced and discussed.

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“…The value α t = 0.7 was proposed by Pietraszkiewicz [48,49], see also [11]. In [10,11,12] the influence of α s and α t on the solution is investigated numerically for several boundary-value problems.…”

Section: On the Constitutive Equations Of Micropolar Shellsmentioning

confidence: 99%

“…Numerical algorithms for solution of the reduced systems of nonlinear equations. For example, it can be done within the framework of the finite element method, see for example the numerical results in [10,11,12]. 3.…”

Section: Principle Peculiarities Of the Micropolar Shell Theorymentioning

confidence: 99%