Sensitivity analysis for transient heat conduction in a solid body ?Part I: External boundary modification

Dems, K.; Rousselet, Bernard

doi:10.1007/bf01197711

Cited by 13 publications

(9 citation statements)

References 11 publications

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“…with proper conditions on interface Γ s following from differentiation of interface conditions (6), (8) or (9). When the finite element approach is used in analyzing the thermal behavior of structure, the description of additional heat transfer problems follows from differentiation of (3) and takes the form:…”

Section: Sensitivity Analysis For Response Functionalsmentioning

confidence: 99%

“…Recently, there has been a great deal of interest in methods of calculating the sensitivity of global behavioral response or local quantities with respect to shape and material variations for a wide class of boundary-value problems. The present paper constitutes an extension of previous author's works in this area [1][2][3][4][5][6][7][8][9]. The multi-phase structure can be subjected to purely thermal or mechanical or combined thermo-mechanical boundary conditions and the variation of an arbitrary thermal or mechanical functional describing the structural quality is considered with respect to shape of interface separating the different phases of structural material.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and design of thermo-mechanical interfaces

Dems¹,

Mróz²

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. An elastic structure subjected to thermal and mechanical loading with prescribed external boundary and varying internal interface is considered. The different thermal and mechanical nature of this interface is discussed, since the interface form and its properties affect strongly the structural response. The first-order sensitivities of an arbitrary thermal and mechanical behavioral functional with respect to shape and material properties of the interface are derived using the direct or adjoint approaches. Next the relevant optimality conditions are formulated. Some examples illustrate the applicability of proposed approach to control the structural response due to applied thermal and mechanical loads.

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Section: Sensitivity Analysis For Response Functionalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis and design of thermo-mechanical interfaces

Dems¹,

Mróz²

2012

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…Sluzalek and Kleiber [11] discuss the material derivative approach for non linear steady state heat conduction, Dems et al [12] use it to obtain the first and second derivatives of an objective function by both sensitivity and adjoint method. In a set of two papers Dems and Rousselet [13,14] discuss sensitivity analysis for transient heat conduction and consider shape parameters for external boundaries as well as for internal interfaces between two materials. They use an analytical mapping.…”

Section: Introductionmentioning

confidence: 99%

A continuous Lagrangian sensitivity equation method for incompressible flow

Charlot

Étienne

Pelletier

2012

Journal of Computational Physics

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“…In Refs. [9,10,[21][22][23][24][25][26], variational continuum adjoint methods for shape sensitivity analysis of transient heat conduction problems are presented without elaborating on the time integration schemes. There are also cases where the problems associated with typical time integration approaches may not appear, e.g., in Ref.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

2020

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In structural design optimization involving transient responses, time integration scheme plays a crucial role in sensitivity analysis because it affects the accuracy and stability of transient analysis. In this work, the influence of time integration scheme is studied numerically for the adjoint shape sensitivity analysis of two benchmark transient heat conduction problems within the framework of isogeometric analysis. It is found that (i) the explicit approach (β = 0) and semi-implicit approach with β < 0.5 impose a strict stability condition of the transient analysis;(ii) the implicit approach (β = 1) and semi-implicit approach with β > 0.5 are generally preferred for their unconditional stability; and (iii) Crank-Nicolson type approach (β = 0.5) may induce a large error for large time-step sizes due to the oscillatory solutions. The numerical results also show that the time-step size does not have to be chosen to satisfy the critical conditions for all of the eigen-frequencies. It is recommended to use β % 0:75 for unconditional stability, such that the oscillation condition is much less critical than the Crank-Nicolson scheme, and the accuracy is higher than a fully implicit approach.

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Sensitivity analysis for transient heat conduction in a solid body ?Part I: External boundary modification

Cited by 13 publications

References 11 publications

Analysis and design of thermo-mechanical interfaces

Analysis and design of thermo-mechanical interfaces

A continuous Lagrangian sensitivity equation method for incompressible flow

An isogeometric numerical study of partially and fully implicit schemes for transient adjoint shape sensitivity analysis

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