Kinematic models of refined theories concerning composite beams, plates, and shells

Lur'e, S. A.; Shumova, N. P.

doi:10.1007/bf02313861

Cited by 8 publications

(5 citation statements)

References 4 publications

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“…The generalization of the adopted model of bending of the sandwich panel proposed in [2] permits us to correct the change of the transverse stresses over the thickness of the filler midlayer. Analytically, the model in [2] becomes complicated by an order of magnitude, and then the agreement of the displacement fields necessary for their approximation [3] is not sufficiently substantiated. The stresses are calculated using the developed numerical method.…”

Section: According To the Relationships Derived In [1] Transverse Nomentioning

confidence: 99%

A refined model for three-point bending of sandwich panels 2. Transverse stresses

Polyakov¹,

Zhigun²,

Shlitsa³

et al. 1998

Mech Compos Mater

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According to the relationships derived in [1] Among the problems associated with the determination of the transverse stresses z n and a z in thin-walled elements of structures of layered composites in bending, the effect of the applied load on the distribution and magnitude of these stresses has not been sufficiently studied. For the surface loads assigned by smooth functions, account of the transverse deformation of a structural element is important only for evaluating the deflections if the relative parameters of the wall thinness (h//) 2 and shear rigidity Gzz/E x are values of the same order. In estimating the greatest values of the transverse stresses, the thinness factor is the governing one, and account of these stresses in the calculation of the bending strength is practically unnecessary. It is necessary to take into consideration the transverse stresses at loading by point forces, as well as in the local area near the edges of the layered structure.An investigation of the stress concentration around the point force, based on the numerical solution of the equations of elasticity theory with respect to the layered character of the structure, is a complicated problem including a labor-consuming analysis of the stress fields with changes in various parameters of the model. The problem is simplified due to the applied approach [1], which allows us to obtain analytical expressions of the displacements and layer curvatures in three-point bending for a three-layered model of 0 0 sandwich type. Since the terms depending on the stresses ~,, and cy z in the midlayer of the compliant filler contribute most to the potential bending energy on the part of the transverse stresses, the values of these stresses in the face layers of the sandwich panel are neglected. We consider the transverse stresses only in the midlayer of the panel, as the face layer with thickness of an order of magnitude smaller than that of the plane is traditionally characterized as a "membrane" element of the sandwich. However, when the point forces areInstitute of Polymer Mechanics.

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Section: According To the Relationships Derived In [1] Transverse Nomentioning

confidence: 99%

A refined model for three-point bending of sandwich panels 2. Transverse stresses

Polyakov¹,

Zhigun²,

Shlitsa³

et al. 1998

Mech Compos Mater

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“…FSDT Equivalent first-order shear deformation theory, shear correction factor of 5/6 is assumed. Reddy and Robbins (1994), Lur'e, and Shumova (1996), Noor et al (1996), Altenbach (1998), Khandan et al (2012) and Kapuria and Nath (2013) and the book by Reddy (2003) are cited among many others, wherein a broad discussion of this matter can be found. However a brief description must be given to justify accuracy and computational costs that differ greatly.…”

Section: Acronymmentioning

confidence: 99%

Free Vibration of flexible soft-core sandwiches according to layerwise theories differently accounting for the transverse normal deformability

Icardi

Urraci

2019

Lat. Am. j. solids struct.

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This study aims to generalize a previously developed accurate and inexpensive 3-D zigzag theory up to an arbitrary representation form and to determine which simplifications are yet accurate in determining transverse shear and normal stress/deformation effects on vibrations of soft-core sandwiches with not moving middle/neutral plane (pumping). Natural frequencies are calculated using displacements assumed differently across the thickness, having fixed d.o.f., not yet explored forms of representation and zigzag functions differently accounting for the transverse normal deformability and that partially or fully fulfill physical constraints. Applications are presented for sandwich plates and beams with length-to-thickness ratios and material properties of faces and core varying within an industrial range, for which layerwise effects are very important and so suited to the evaluation of theories. Analytical solutions are found using the same trial functions and expansion order for all theories, so to evaluate their accuracy under the same conditions. The choice of the representation form and of zigzag functions is shown immaterial if displacement field coefficients are recomputed across the thickness by enforcing the fulfillment of all physical constraints (using symbolic calculus). Furthermore, it is shown that assigning a specific role to each coefficient is immaterial, as well as exchanging the order of representation of in-plane and transverse displacement components and even that zigzag functions could be omitted. This no longer occurs for lower-order theories with only a partial fulfillment of constraints. Pumping motions are highlighted as the first modes, which require the theories much accurately accounting for transverse normal deformability. Keywords Composite and sandwich plates and beams, interlaminar transverse shear and normal stress continuity, Navier's and 3D finite element analysis (FEA) solutions, free vibration behavior, different zigzag functions, various form of representation of variables 1 INTRODUCTION As it is well known, sandwiches find continuously increasing applications in aerospace, naval and terrestrial applications owing to superior specific strength and stiffness than traditional materials. Free Vibration of flexible soft-core sandwiches according to layerwise theories differently accounting for the transverse normal deformability Ugo Icardi et al.

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“…All the field variables together with their derivatives are assumed to be exist, single-valued and continuous functions of the space coordinates and time in the laminae region with the absence of any kind of singularities, and also, they are assumed, as usual, not varied widely across the thickness. Lur'e and Shumova (1996) examined the kinematic models used for construction of energetically consistent equations of laminated structural elements, as did Vasiliev and Lurie (1992), Reddy andRobbins (1994), andReddy (2004). As before, a kinematic type of models is chosen, and the mechanical displacements, and the electric and magnetic potentials are taken as a basis for the derivation of laminae equations.…”

Section: Basic Field Variablesmentioning

confidence: 99%

On the fundamental equations of electromagnetoelastic media in variational form with an application to shell/laminae equations

Altay¹,

Dökmeci²

2010

International Journal of Solids and Structures

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a b s t r a c tThe fundamental equations of elasticity with extensions to electromagnetic effects are expressed in differential form for a regular region of materials, and the uniqueness of solutions is examined. Alternatively, the fundamental equations are stated as the Euler-Lagrange equations of a unified variational principle, which operates on all the field variables. The variational principle is deduced from a general principle of physics by modifying it through an involutory transformation. Then, a system of two-dimensional shear deformation equations is derived in differential and fully variational forms for the high frequency waves and vibrations of a functionally graded shell. Also, a theorem is given, which states the conditions sufficient for the uniqueness in solutions of the shell equations. On the basis of a discrete layer modeling, the governing equations are obtained for the motions of a curved laminae made of any numbers of functionally graded distinct layers, whenever the displacements and the electric and magnetic potentials of a layer are taken to vary linearly across its thickness. The resulting equations in differential and fully variational, invariant forms account for various types of waves and coupled vibrations of one and two dimensional structural elements as well. The invariant form makes it possible to express the equations in a particular coordinate system most suitable to the geometry of shell (plate) or laminae. The results are shown to be compatible with and to recover some of earlier equations of plane and curved elements for special material, geometry and/or effects.

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Kinematic models of refined theories concerning composite beams, plates, and shells

Cited by 8 publications

References 4 publications

A refined model for three-point bending of sandwich panels 2. Transverse stresses

A refined model for three-point bending of sandwich panels 2. Transverse stresses

Free Vibration of flexible soft-core sandwiches according to layerwise theories differently accounting for the transverse normal deformability

On the fundamental equations of electromagnetoelastic media in variational form with an application to shell/laminae equations

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