Extension of the Stroh formalism to the analysis of bending of anisotropic elastic plates

Lü, Peng; Mahrenholtz, O.

doi:10.1016/0022-5096(94)90069-8

Cited by 32 publications

(24 citation statements)

References 6 publications

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“…The vanishing of the 4 Â 4 determinant in the eigenrelation (20) gives a polynomial of order eight in l, from which the eight eigenvalues can be obtained, and the associated eigenvectors can be determined from (20). It should be pointed out that the eigen-polynomial derived from (20) is exactly the same as the one obtained from (3.9) of [9]. By substituting (17), (13a) and (14) into (9a), we have…”

Section: Basic Equations and Definitionsmentioning

confidence: 89%

“…The constitutive relations of the anisotropic plate with bending-extension coupling are given by, s. [17,9], …”

Section: Basic Equations and Definitionsmentioning

confidence: 99%

“…For stress-or displacement-only boundary value problems, such as stress-free hole or rigid inclusion boundaries, however, the hybrid formalism is not a good choice due to the mixed nature of its eigenrelations. On the other hand, the mathematical structures of the existing displacement formalisms [8][9][10] are also not perfect for the latter problems and need to be improved as mentioned above.…”

Section: Introductionmentioning

confidence: 97%

“…The reason for that may be partly due to the fact that the interests of researchers familiar with the Stroh formalism were initially mainly focused on the problems concerning physical and material sciences. It seems that the first effort to extend the Stroh formalism to the problem of anisotropic plate bending was reported in [8,9]. The studies began with two in-plane displacements and two slope functions, which had to satisfy three equilibrium equations as well as a relation between the slope functions.…”

Section: Introductionmentioning

confidence: 99%

“…For problems of anisotropic plates with bending only and bending-extension coupling, the corresponding singular solutions have been derived based on the Lekhnitskii-type formalisms in [2, 14,15], respectively. The problem has also been discussed in [16] based on the formulas derived in [9]. As an important application of the Stroh-type formalism, the problem is considered in this paper.…”

Section: Introductionmentioning

confidence: 99%

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A Stroh-type formalism for anisotropic thin plates with bending-extension coupling

Lü

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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In the present paper, a complete Stroh-type formalism for the problems of anisotropic thin plates with bending-extension coupling is developed. The formalism includes two forms, the hybrid formalism and the displacement formalism, which are related to each other. Both the hybrid and the displacement formalisms with their respective structures of eigenrelations and general solutions are perfectly alike to the Stroh formalism for plane strain problems. Therefore, most of the identities and mathematical techniques developed for the Stroh formalism can be conveniently transferred and applied to the two formalisms. The hybrid Stroh-type formalism is suitable for mixed boundary value problems, while the displacement Stroh-type formalism is suitable for displacement-or stress-only boundary value problems. As applications of the Stroh-type formalism, several problems are solved. One is the derivation of singular solutions for an anisotropic thin plate with bending-extension coupling. The other is the analysis of an anisotropic plate with a hole solved by the displacement formalism.

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Section: Basic Equations and Definitionsmentioning

confidence: 89%

“…The constitutive relations of the anisotropic plate with bending-extension coupling are given by, s. [17,9], …”

Section: Basic Equations and Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Stroh-type formalism for anisotropic thin plates with bending-extension coupling

Lü

2004

Archive of Applied Mechanics (Ingenieur Archiv)

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Structure and properties of the fundamental elastic plate matrix

Cheng

Reddy

2005

Z Angew Math Mech

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This work presents further development of the octet formalism established by the authors for the classical Kirchhoff anisotropic plate theory. The structure of the fundamental elastic plate matrix is fully explored and the explicit expression is provided. The matrices N2 and N3 are proved to be positive semi‐definite. Thus, H and L are positive definite. Further studies are concerned with a rotated coordinate system. The transform relation between the eigenvectors in the original and the rotated coordinate system is given. The fundamental elastic plate matrix associated with the eigenrelation referring to the dual coordinate systems, NΘ, is studied. The major properties that hold in the Stroh sextic formalism for generalized plane strain problems are also valid in the octet formalism for thin plate bending problems. In particular, we generalize a property in Stroh's formalism for any non‐semisimple matrix NΘ. We show a new property in the octet formalism. The non‐semisimple cases of NΘ are discussed. Finally, we make it transparent that the mixed/hybrid formalism of others is precisely one of sixteen permuted forms of the octet formalism.

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