Exact solution for thick laminated closed cylindrical shells with two clamped edges

Jun, Fan; Ding, Ke

doi:10.1016/0307-904x(93)90073-p

Cited by 10 publications

(19 citation statements)

References 5 publications

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“…Very few approximate analytical solutions of the 3D elasticity equations have been reported for bending of laminated plates. Fan and Sheng [2] presented an analytical 3D solution for bending of laminated orthotropic plates with clamped edges, wherein the boundary conditions were satisfied only at discrete points along the edges. Vel and Batra [3] used the EshelbyStroh formalism to obtain a series solution for the cylindrical bending of laminated elastic plates subjected to arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

Kapuria¹,

Kumari

2012

Journal of Applied Mechanics

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In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

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Section: Introductionmentioning

confidence: 99%

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

Kapuria¹,

Kumari

2012

Journal of Applied Mechanics

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“…The geometric parameter ρ = R c + r cos θ follows from the radius of the tube curvature R c and the radial coordinate of the tube r. As can be seen, the displacements can be divided into a part independent of ρ, a linear-dependent, and a nonlinear-dependent part. The coefficients in (65) are…”

Section: Curved Tube Under Bending According To Sarvestani Et Almentioning

confidence: 99%

“…For equation (65) the subscripts n, which correspond to the order of the coefficients and displacements, vanish and for the later equation ( 68) they are used with n = 0-3. There is no exact solution for the Navier equations of toroidal elasticity, which is why the solution is approximated by the method of successive approximation.…”

Section: Curved Tube Under Bending According To Sarvestani Et Almentioning

confidence: 99%

Review of elasto-static models for three-dimensional analysis of thick-walled anisotropic tubes

Kastenmeier,

Siegl,

Ehrlich

et al. 2023

Journal of Composite Materials

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Most shell or beam models of anisotropic tubes under bending have no validity for thick-walled structures. As a result, the need to develop three-dimensional formulations which allow a change in the stress, strain and displacement distributions across the radial component arises. Basic formulations on three-dimensional anisotropic elasticity were made either stress- or displacement-based by Lekhnitskii or Stroh on plates. Lekhnitskii also was the first to expand these analytical formulations to tubes under various loading conditions. This paper presents a review of the stress and strain analysis of tube models using three-dimensional anisotropic elasticity. The focus lies on layered structures, like fiber-reinforced plastics, under various bending loads, although the basic formulations and models regarding axisymmetric loads are briefly discussed. One section is also dedicated to the determination of an equivalent bending stiffness of tubes.

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“…In addition, the boundary conditions are set to be simply supported or clamped edges for plates subjected to Load I and Load II. We assume that the interfacial imperfection coefficients S zc vanish hereunder to avoid the material penetration phenomenon at the two interfaces [26, 27]. To simplify matters, we also suppose S rc j = S rc j + 1 and S rq j = S rq j + 1 in the following numerical examples.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Among analytical methods, the state vector approach is useful to solve multilayered structures under multi-field and multi-working conditions. Using appropriate stress or displacement functions, Fan [27], Sheng and Fan [28, 29], Sheng [30] and Ye [31, 32] obtained three-dimensional (3D) analytical solutions for thin, moderately thick, and thick multilayered plates and shells with different structural boundary conditions. On the basis of 3D displacement method and propagator matrix method, Gao et al [33] studied the frequency of free vibration of simply supported piezoelectric rectangular plates.…”

Section: Introductionmentioning

confidence: 99%

Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

Huang

Zhao

Feng

2021

Mathematics and Mechanics of Solids

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A three-dimensional (3D) electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal (QC) circular plates with simply supported or clamped boundary conditions is presented through a state vector approach. Both perfect and imperfect bonds between the layers are considered by adjusting the parameter sets in the model. Governing equations for the plates subjected to electric or elastic load on the bottom surfaces are derived using the state equations and the propagator matrix method. We explicitly obtain the analytical solution by writing the physical variables as Bessel series expansions and polynomial functions with respect to the radial coordinate. The solution is validated by comparing the numerical results with the 3D ﬁnite element analysis. The basic physical quantities of the plates in the phonon, phason, and electric fields are computed in the numerical examples. Result shows that the QC layers as coatings decrease the deflection in the phonon and phason fields of plates. The phonon–phason coupling elastic modulus and piezoelectric constant produce positive and negative effects on the magnitudes of stresses. Besides, compliance coefficients of the weak interface in the phonon field contribute more to the variations than those in the phason field.

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Exact solution for thick laminated closed cylindrical shells with two clamped edges

Cited by 10 publications

References 5 publications

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

Review of elasto-static models for three-dimensional analysis of thick-walled anisotropic tubes

Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

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