A novel approach to the solution of the tensor equation AX+XA=H

Rosati, Luciano

doi:10.1016/s0020-7683(99)00053-0

Cited by 19 publications

(12 citation statements)

References 20 publications

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“…which is a result proved in, among others, [16]. Assuming that this condition is satisfied, the desired inverse is…”

Section: An Explicit Expression For (S ¢ I + I ¢ S) J1mentioning

confidence: 52%

Derivatives of the Stretch, Rotation and Exponential Tensors in n-Dimensional Vector Spaces

Jog

2006

J Elasticity

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We present a solution for the tensor equation TX + XT T = H, where T is a diagonalizable (in particular, symmetric) tensor, which is valid for any arbitrary underlying vector space dimension n. This solution is then used to derive compact expressions for the derivatives of the stretch and rotation tensors, which in turn are used to derive expressions for the material time derivatives of these tensors. Some existing expressions for n = 2 and n = 3 are shown to follow from the presented solution as special cases. An alternative methodology for finding the derivatives of diagonalizable tensor-valued functions that is based on differentiating the spectral decomposition is also discussed. Lastly, we also present a method for finding the derivatives of the exponential of an arbitrary tensor for arbitrary n. (2000): 74B99. Mathematics Subject Classifications

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“…which is a result proved in, among others, [16]. Assuming that this condition is satisfied, the desired inverse is…”

Section: An Explicit Expression For (S ¢ I + I ¢ S) J1mentioning

confidence: 52%

Derivatives of the Stretch, Rotation and Exponential Tensors in n-Dimensional Vector Spaces

Jog

2006

J Elasticity

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“…For the case of symmetric A, this equation has been solved by several researchers (Sidoroff, 1987;Schiedler, 1994;Hoger and Carlson, 1984;Rozati, 2000). In the present problem A :¼ U T is not in general a symmetric tensor and the solution of Eq.…”

Section: Energy Pairs In the Micropolar Mediamentioning

confidence: 90%

Energy pairs in the micropolar continuum

Ramezani

Naghdabadi

2007

International Journal of Solids and Structures

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In this paper, the concept of energy pairs in the micropolar continuum is introduced. A brief review of the micropolar continuum theory is presented for using in the subsequent derivations. A mathematical Lagrangian strain and a wryness tensor for the micropolar continuum are introduced. Using the first law of thermodynamics and for isothermal processes, the power of deformation is obtained and the energy pairs in the Eulerian and Lagrangian descriptions are defined. Also, the micropolar stress and couple stress tensors which are energy pairs to the micropolar Lagrangian strain and wryness measures are determined.

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“…An analogous approach in tensor notation is also possible. However, it leads to a complex system [19] that makes impractical to obtain simple closed form solutions and it is not presented in this paper.…”

Section: Formulationmentioning

confidence: 99%