Reduction of the periodic thermoelastic deformation in truss-structures by design refinements and active loads

Rand, Omri; Givoli, Dan

doi:10.1016/0045-7949(94)00363-8

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…An example of the latter case is the optimal control of linear elastic truss and beam structures, where a structure is typically represented by its finite element stiffness and mass matrices (of a finite dimension), and the whole solution process is performed in the time (or frequency) domain. See, e.g., [2,3] for applications in optimal control of rotating space structures.…”

Section: Introductionmentioning

confidence: 99%

A direct approach to the finite element solution of elliptic optimal control problems

Givoli

1999

Numer. Methods Partial Differential Eq.

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A general framework is developed for the finite element solution of optimal control problems governed by elliptic nonlinear partial differential equations. Typical applications are steady-state problems in nonlinear continuum mechanics, where a certain property of the solution (a function of displacements, temperatures, etc.) is to be minimized by applying control loads. In contrast to existing formulations, which are based on the ''adjoint state,'' the present formulation is a direct one, which does not use adjoint variables. The formulation is presented first in a general nonlinear setting, then specialized to a case leading to a sequence of quadratic programming problems, and then specialized further to the unconstrained case. Linear governing partial differential equations are also considered as a special case in each of these categories.

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Section: Introductionmentioning

confidence: 99%

A direct approach to the finite element solution of elliptic optimal control problems

Givoli

1999

Numer. Methods Partial Differential Eq.

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“…Models for transient thermoelastic FEM are developed and compared with analytical solutions, as presented in Nickell and Sackman (1968) and Ting and Chen (1982). Rand and Givoli (1995) developed a dynamic model thermoelastic for FEM. Formulations of finite elements for thermoelastic damping are obtained from an irreversible entropy flux due to the heat fluxes caused by the variations of volumetric stresses, as presented in Serra and Bonaldi (2009).…”

Section: The Coupled Thermomechanicalmentioning

confidence: 99%

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Cavalcante

Maciel

Greco

et al. 2017

Lat. Am. j. solids struct.

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The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

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Reduction of the periodic thermoelastic deformation in truss-structures by design refinements and active loads

Cited by 2 publications

References 13 publications

A direct approach to the finite element solution of elliptic optimal control problems

A direct approach to the finite element solution of elliptic optimal control problems

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

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