A General Theory of Strength for Anisotropic Materials.

Tsai, Stephen W.; Wu, Edward M.

doi:10.21236/ada306350

Cited by 477 publications

(711 citation statements)

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“…On the other hand, the strength theories of materials (see, e.g., [27][28][29]), in particular, require sufficiently accurate values for stresses as well. By the use of some other methods, stresses can be calculated more accurately as will be reported later.…”

Section: On Resultsmentioning

confidence: 99%

Stress and strain analysis in elastic laminated composite beams

Dökmeci

1973

J Elasticity

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A detailed theoretical analysis of stress and strain in fiber-reinforced, laminated composite beams is presented within the framework of three-dimensional theory of thermo-elastodynamics. Each of reinforcing and matrix layers is made of different anisotropic material and is of different constant thickness. By the use of a variational theorem, the fully non-linear governing equations are consistently obtained for the case when the displacement components of each layer are taken to vary linearly over the cross-section of the layer. Then the linear version of the resulting equations, including the uniqueness of its solution is given, and the general results are briefly discussed. ZUSAMMENFASSUNGIn der vorliegenden Abhandlung wird eine detaillierte Spannungs-und Verzerrungsuntersuchung von faserverst/irkten laminierten Balken innerhalb der dreidimensionalen thermo-elastodynamischen Theorie durchgefiihrt. Ffir jede Verst/irkungs-und Bindeschicht wird unterschiedliches anisotropes Verhalten und unterschiedliche Schichtst/irke vorausgesetzt. Unter Annahme eines linearen Verlaufs der im Querschnitt liegenden Verformungskomponenten fiber jede einzelne Schicht werden mit Hilfe eines Satzes der Variationsrechnung die vollst/indigen nichtlinearen Grundgleichungen abgeleitet. Damit ist auch die linearisierte Form der Gleichungen mit eindeutiger L6sung bestimmt. Eine kurze Untersuchung der Ergebnisse in ihrer allgemeinen Form ist angeschlossen.

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Section: On Resultsmentioning

confidence: 99%

Stress and strain analysis in elastic laminated composite beams

Dökmeci

1973

J Elasticity

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“…These criteria generally follow a quadratic expression which represents a closed surface. Dealing with anisotropic materials, the rotated and translated ellipsoid of Tsai-Wu (Tsai and Wu 1971) is the most common failure surface. The general quadratic expression for orthotropic materials can be written as:…”

Section: Van Der Put's Mixed Failure Criterion For Woodmentioning

confidence: 99%

Influence of orientation and number of layers on the elastic response and failure modes on CLT floors: modeling and parameter studies

et al. 2016

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International audienceIn the present paper, the bending behavior of Cross Laminated Timber panels is investigated by means of the linear elastic exact solution from Pagano (1970; 1969). The resulting stresses are the input for a wood failure criterion , which can point out the first-crack load and the respective dominant failure mode. Heterogeneous layers are mod-eled as equivalent and homogeneous layers. This simplified and deterministic modeling gives results in good agreement with a reference experimental test. A comparison is made with respect to the panel's global stiffness and failure stages within the apparent elastic stage. Finally, parameter studies are carried out, in order to quantify CLT limitations and advantages. The effect of varying properties like the panel's slenderness, orientation of transverse layers and number of layers for a fixed total thickness are investigated

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“…with the last criterion from Tsal and Wu (1971). More generally, some damage parameters may be used.…”

Section: Optimal Design For Strengthmentioning

confidence: 99%

Some general optimal design results using anisotropic, power law nonlinear elasticity

Podersen

1998

Structural Optimization

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Recent results on optimal design with anisotropic materials and optimal design of the materials themselves are in most cases based on the assumption of linear elasticity. We shall extend these results to the nonlinear model classified as powerlaw elasticity. These models return proportionality between elastic strain energy density and elastic stress energy density. This is shown to imply localized sensitivity analysis for the total elastic energy, and for a number of optimal design problems this immediately gives practical, general results.For two-and three-dimensional problems the effective strain and the effective stress are defined from an energy consistent point of view, and it is shown that a definition generalizing the von Mises stress must be used. The optimization criterion of uniform energy density also holds for nonlinear materials, and several general conclusions can be based on this fact. Applications to size design illustrate this.For stiffness optimization the ultimate optimal material design problem is addressed. The validity of recent results are extended to nonlinear materials, and a simple proof based on constraint on the Frobenius norm is given. We note that the optimal material is orthotropic, that principal directions of material, strain and stress are aligned, and that there is no shear stiffness. In reality, the constitutive matrix only has one nonzero eigenvalue and the material therefore has stiffness only in relation to the specified strain condition. Results related to orientational design with.orthotropic materials are also focused on.With respect to strength optimization, i.e. the more difficult problem with local constraints, we shall comment on the influence of the different strength criteria.

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A General Theory of Strength for Anisotropic Materials.

Cited by 477 publications

References 0 publications

Stress and strain analysis in elastic laminated composite beams

Stress and strain analysis in elastic laminated composite beams

Influence of orientation and number of layers on the elastic response and failure modes on CLT floors: modeling and parameter studies

Some general optimal design results using anisotropic, power law nonlinear elasticity

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