Stress-free displacement control of structures

Nyashin, Y.I.; Лохов, В А; Ziegler, Franz

doi:10.1007/s00707-004-0191-1

Cited by 19 publications

(8 citation statements)

References 10 publications

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“…A novel and efficient solution method for modelling and control of static or quasi-static stress and deformation by eigenstrain is ilustrated based on the theorem on decomposition of eigen-strain, [12] and [14]. A straightforward method for the determination of the dimensions in energy space of eigenstrain, subspaces of impotent eigenstrain and nilpotent eigenstrain, for discrete (trusses) or discretized structures (FEM) is discussed.…”

Section: Resultsmentioning

confidence: 99%

“…Accordingly, the space is thus called energy space. For discretized structures, two mutual orthogonal finite dimensional sub-spaces exist, i. e., any tensor of eigenstrain ε ∈ H existing in a body can be uniquely decomposed into its impotentε * and nilpotentε * * constituents, see [12] and [14],…”

Section: Eigenstrain-induced Small Vibrations: Dynamic Shape Controlmentioning

confidence: 99%

“…The mass is lumped to the nodes, stiffness EA of the member rods is assumed to be constant. Since the load case is prescribed, we can directly calculate the quasi-static strains in the smart member rods, [21], and impose these strains as impotent eigenstrains, thus preserving the quasi-static member forces N For a rigorous formulation of the main theorem on eigenstress and eigenstrain, the Hilbert function space H is introduced [12], [14], as the space of second rank symmetric tensors where the components are real functions of spatial coordinates in the function space L 2 . Assume, that the eigenstrain tensors are the elements of the Hilbert space.…”

Section: Eigenstrain-induced Small Vibrations: Dynamic Shape Controlmentioning

confidence: 99%

“…In [12] the crucial, unique decomposition of an eigenstrain tensor, e.g. of piezoelectric strain, is performed by means of the scalar product measure in Hilbert functional space, rendering its impotent part that does not produce stress, see also [13] and [14], and its complement, the nilpotent eigenstrain that renders stresses but does not produce deformation, see [10], [12] and [15].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

Ziegler¹

2010

Mechanics and Model-Based Control of Smart Materials and Structures

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Vibrations may shorten the lifetime of structures and machines, cause discomfort in many cases (noise radiation) and are totally unwanted in precision engineering. The latter requires also static shape control. The method of unique decomposition of eigenstrains into two constituents, namely in impotent eigenstrains, that do not cause stress and in the complementary nilpotent eigenstrains that do not induce any deformation in the linear elastic solid is considered in detail. These two complete classes of eigenstrains render optimal solutions by keeping shape and stress-control problems well separated. Assuming a common time function of the dynamic load, a novel approach is addressed to annihilate the forced vibrations. This optimal benchmark solution may serve the purpose in practical application to select properly shaped actuator patches and the control current.

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Section: Resultsmentioning

confidence: 99%

Section: Eigenstrain-induced Small Vibrations: Dynamic Shape Controlmentioning

confidence: 99%

Section: Eigenstrain-induced Small Vibrations: Dynamic Shape Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

Ziegler¹

2010

Mechanics and Model-Based Control of Smart Materials and Structures

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“…В некоторых случаях полем напряжений можно управлять [9][10][11][12]. В любом случае необходимо как можно раньше исправлять патологии зубочелюстной системы.…”

Section: Introductionunclassified

Биомеханический Анализ Мостовидного Протеза Для Замещения Дефектов Зубного Ряда, Осложненных Вторичными Деформациями

Тропин¹,

Лохов²,

Старкова³

et al. 2015

Российский журнал биомеханики

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Statement and solution of optimal problems for independent stress and deformation control by eigenstrain

2009

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The method of unique decomposition of eigenstrain into two constituents, namely in impotent eigenstrain, that does not cause stress and in the complementary nilpotent eigenstrain that does not induce any deformation in the linear elastic solid is considered in detail. Decomposition is performed in the Hilbert (energy) function space. These two complete classes of eigenstrains render optimal solutions by keeping shape and stress‐control problems well separated. Such an optimization is found to be of crucial importance in the design of smart structures, which can adapt to altering conditions. Benchmark solutions of both, shape control and optimal redistribution of elastic load stresses in discretized smart structures illustrate the power of the novel method and its convenience of application. Further, the problem of residual stress control past hot rolling of I‐beams is solved: the theorem on decomposition provides the crucial tool to define the required control parameters for forced cooling‐down with the goal of producing a favourable residual stress state as close as possible to a predefined (optimal) stress state. The latter is exemplarily selected to increase the buckling strength of such columns with given slenderness ratio.

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Stress-free displacement control of structures

Cited by 19 publications

References 10 publications

The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

The basis of optimal active(static and dynamic) shape- and stress-control by means of smart materials

Биомеханический Анализ Мостовидного Протеза Для Замещения Дефектов Зубного Ряда, Осложненных Вторичными Деформациями

Statement and solution of optimal problems for independent stress and deformation control by eigenstrain

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