Optimal Design of Supports of Elastic Structures Subjected to Loads and Initial Distortions

Garstecki, Andrzej; Mróz, Z.

doi:10.1080/08905458708905108

Cited by 22 publications

(9 citation statements)

References 6 publications

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“…The conditions in the present paper are obtained via a different and simpler path than the one followed in the papers by Rozvany and Mr6z (1977), Mr6z (1978, 1979), and confirm the results obtained therein. The problem of the optimum location and stiffness of supports of elastic frames has been studied by MrSz and Lekszycki (1981) and Garstecki and Mr6z (1987). The reader is referred to a book by Rozvany (1989) for a survey of the optimal design of beams with unspecified actions or reactions and to the classical paper by Keller and Niordson (1966) for the optimal design of columns with selfweight using the crosssectional area and shape as design variables.…”

Section: Introductionmentioning

confidence: 98%

Minimum stiffness of optimally located supports for maximum value of column buckling loads

Olhoff

Åkesson

1991

Structural Optimization

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A b s t r a c t The problem of maximizing the buckling load of Bernoulli-Euler columns, with their continuously distributed selfweight taken into account, is considered in cases where the stiffnesses and positions of discrete lateral spring supports are used as design variables. Necessary conditions for optimum support stiffness and position are derived, and they are discussed in the light of some classical results. Several numerical examples are presented. I n t r o d u c t i o nIt is well-known (Courant and Hilbert 1953) that optimum locations of a given number of rigid interior lateral supports which maximize the fundamental natural frequency of transverse vibrations of a string or beam, or the bifurcation load of an axially compressed column, are nodal points of an appropriate higher-order vibration of buckling mode of the original structure.In a recent paper on transversely vibrating beams, /~ke-sson and Olhoff (1988) demonstrated how the stiffnesses of supports placed in the described way may be reduced to finite minimum values without a decrease of the fundamental natural frequency. Thus optimum characteristics can be maintained at a reduced cost since a decrease of support stiffnesses normally implies a cheaper structure. However, if the support stiffnesses are decreased below the aforementioned minimum values, which are problem-dependent, then the fundamental frequency decreases from its maximum value. Also the optimum positions of the supports will no longer be the nodal points mentioned, but will be governed by different conditions.In the present paper we show that the problem of the optimal support of columns exhibits features similar to those of vibrating beams and we determine the optimum positions and stiffnesses of a set of discrete lateral supports in several problems where the selfweight of a vertical column is taken into account.In Section 2, we formulate the buckling eigenvalue problem, establish the pertinent Rayleigh quotient, and derive necessary conditions for the optimum stiffness and location of flexible lateral supports by variational analysis. In Section 3, these conditions are discussed relative to some known conditions for optimally placed rigid lateral supports by way of the detailed example of a cantilever column under pure selfweight loading, and we identify the aforementioned features.

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Section: Introductionmentioning

confidence: 98%

Minimum stiffness of optimally located supports for maximum value of column buckling loads

Olhoff

Åkesson

1991

Structural Optimization

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“…It is worth adding that in general, according to [5], we assume both the initial strain field q i which is kinematically inadmissible and initial stress field Q i which is statically inadmissible. In effect elastic strain q e and stress Q e (4) are induced (Fig.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Later in [8] the adjoint variable method was developed. The influence of the initial distortions on the optimal design of support conditions in beams and frames was studied in [5]. In [6,9] the sensitivity analysis in the case of dynamically loaded structures allowing for variable joint parameters has been presented.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity analysis of sandwich beams and plates accounting for variable support conditions

Studziński¹,

Pozorski²,

Garstecki³

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper addresses the problems of the sensitivity analysis and optimal design of multi-span sandwich panels with a soft core and flat thin steel facings. The response functional is formulated in a general form allowing wide practical applications. Sensitivity gradients of this functional with respect to dimensional, material and support parameters are derived using adjoint variable method. These operators account for the jump of the slope of a Timoshenko beam or a Reissner plate at the position of concentrated active load or reaction, thus extending the sensitivity operators known in literature. The jump of slope is the effect of shear deformation of the core. Special attention is focussed on sensitivity and optimisation allowing for variable support position and stiffness, because local phenomena observed in supporting area of sandwich plates often initiate failure mechanisms. Introducing optimally located elastic supports allows to reduce the unfavourable influence of temperature on the state of stress. Several examples illustrate the application of derived sensitivity operators and demonstrate their exactness.

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“…The thermal actions are distortions. The influence of the initial distortions on the optimal design of support conditions in beams and frames was studied in [8]. In the case of statically undetermined systems, deformations induced by temperature are constrained.…”

Section: Introductionmentioning

confidence: 99%

Static response of thermally loaded sandwich beams with confined horizontal displacements of faces at the supports

Pozorska

Pozorski

2014

J. Appl. Math. Comput. Mech.

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Abstract. The paper examines the problem of the influence of restrictions on freedom of horizontal displacements in thermally loaded sandwich beams. The classical theory of sandwich beams and panels with thin facings and a soft core has been applied. It was assumed that the cross-section of the beam could be asymmetric geometrically and materially. The beam has vertical supports and additional horizontal supports limiting the freedom of horizontal displacements. The supports are linearly elastic and the rigidity of the upper and lower support can be arbitrary. The static problem of single-span beam with support conditions identical at both ends of the beam was solved in the paper. Each of the sandwich facings has been subjected to temperature change. The derived formulas were used in the example illustrating the importance of the problem.

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Optimal Design of Supports of Elastic Structures Subjected to Loads and Initial Distortions

Cited by 22 publications

References 6 publications

Minimum stiffness of optimally located supports for maximum value of column buckling loads

Minimum stiffness of optimally located supports for maximum value of column buckling loads

Sensitivity analysis of sandwich beams and plates accounting for variable support conditions

Static response of thermally loaded sandwich beams with confined horizontal displacements of faces at the supports

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