Transformation of dynamic loads into equivalent static loads based on modal analysis

Choi, Woo-Seok; Park, G. J.

doi:10.1002/(sici)1097-0207(19990910)46:1<29::aid-nme661>3.3.co;2-4

Cited by 13 publications

(15 citation statements)

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“…(11) is a system of linear simultaneous equations with/'variables for sj Therefore, vector s is determined from Eq. (11) and dp(ta) (p > l') is approximated in Eq. (12).…”

Section: Approximation Methodsmentioning

confidence: 99%

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Calculation of equivalent static loads and its application

Choi

Park

2005

Nuclear Engineering and Design

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All the forces in the real world act dynamically on structures. Since dynamic loads are extremely difficult to handle in analysis and design, static loads are usually utilized with dynamic factors. Static loads are especially exploited well in structural optimization where many analyses are carried out. However, the dynamic factors are not determined logically. Therefore, structural engineers often come up with unreliable solutions. An analytical method based on modal analysis is proposed for the transformation of dynamic loads into equivalent static loads (ESLs). The ESLs are calculated to generate an identical displacement field with that from dynamic loads at a certain time. The process is derived and evaluated mathematically by using the modal analysis. Since the exact solution is extremely expensive, some approximation methods are proposed. Error analyses have been conducted for the approximation methods. Standard examples for structural design are selected and solved by the proposed method. Applications of the method to structural optimization are discussed.

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“…(11) is a system of linear simultaneous equations with/'variables for sj Therefore, vector s is determined from Eq. (11) and dp(ta) (p > l') is approximated in Eq. (12).…”

Section: Approximation Methodsmentioning

confidence: 99%

“…A dynamic load is transformed to an ESL set. The ESL set is made to generate the identical displacement field with the one from the dynamic load at an arbitrary time [9][10][11]. The displacement field under the dynamic load can be expressed by the modal analysis in the vibration theory.…”

Section: Introductionmentioning

confidence: 99%

Calculation of equivalent static loads and its application

Choi

Park

2005

Nuclear Engineering and Design

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“…Na segunda metade da década de 90, Choi & Park [14] introduziram um método de aproximação chamado método de carregamentos estáticos equivalentes (Equivalent Static Loads, abreviado por ESL), onde o carregamento dinâmico original também é substituído por carregamentos estáticos. Contudo, neste método, os novos carregamentos devem obrigatoriamente gerar o mesmo campo de resposta que o carregamento dinâmico para toda a análise dinâmica.…”

Section: Carregamentos Estáticos Equivalentesunclassified

“…Em Choi & Park [14] é proposta a transformação de carregamentos dinâmicos em estáticos equivalentes na análise transiente via análise modal. Dois tipos de carregamentos equivalentes, um exato e um aproximado, são deduzidos no artigo e resultados envolvendo estruturas de treliça, viga e pórticos são apresentados.…”

Section: Carregamentos Estáticos Equivalentesunclassified

Otimização Paramétrica De Estruturas Treliçadas Sob a Ação De Cargas Dinâmicas Utilizando O Método Do Carregamento Estático Equivalente

SANTOS¹

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Structural optimization subject to dynamic loading is a challenging problem in many aspects, starting with the large number of constraints that must be respected at all instants of time. Furthermore, the computational cost to evaluate the gradients of these constraints is significantly high and requires a large storage space. In the literature, some methods reduce the number of constraints evaluating at selected instants of time, such as the worst case. Alternatively, a single equivalent functional is constructed to eliminate the time dependence by integrating the violated constraints over time. In this work, the Equivalent Static Load (ESL) method is used, in which the original dynamic problem is reduced into a number of static linear optimization problems with multiple load cases. An attractive feature of this method is the possibility of solving non-linear problems, avoiding the high cost due to repeated structural analyzes and constraint calculations. Classical problems of plane trusses subjected to dynamic loads are solved using the ESL method. The function to be minimized is the truss mass, which is subjected to stress and displacement constraints, where the design variables are the cross-sectional areas of the members. In addition, an interface using ANSYS ® and MATLAB ® was developed for a modular approach, in which finite element analysis and optimization can be performed separately. This process makes possible the optimization of structures that present non-linear behavior from the use of most structural analysis software packages available on the market.

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“…To alleviate some of these issues, constraints such as frequency range, displacement and stresses were sometimes imposed in the algorithms to tailor the structure's dynamic response [24,[27][28][29].…”

Section: Literature Reviewmentioning

confidence: 99%

High Fidelity and Efficient Computations of Dynamic Loads for Multidisciplinary Design Optimization of Flexible Transport Aircraft

Nieto¹

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The current state-of-the-art design optimization of airframes is tightly wounded to its loads analyses as the process is usually conducted employing a deterministic set of critical load cases. The sheer number of scenarios required to estimate the critical loading conditions prevent these two processes from integrating, obstructing the development of a Multidisciplinary Design Optimization (MDO) framework. In this thesis, the problem of high fidelity and efficient estimation of critical dynamic aeroelastic loads is addressed, as a first step, towards the development of an integrated MDO platform for airframes at preliminary and detailed design stages. The method is based on the Kriging metamodeling technique along with the Latin Hypercube scheme for initial sampling and the expected improvement function for subsequent selection of sample points, known formally as the Efficient Global Optimization (EGO) algorithm. Furthermore, different inexpensive metrics, based on the concept of modal contribution factors, are investigated to serve as indicators to determine if a substantial change in the loads has occurred during the design optimization cycle, triggering the requirement for the re-exploration of the loads design space. A case study is presented to evaluate the performance of the proposed methodology versus a full factorial search. A reduction of 84% was achieved in the total time of execution employing the proposed methodology.

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Transformation of dynamic loads into equivalent static loads based on modal analysis

Cited by 13 publications

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Calculation of equivalent static loads and its application

Calculation of equivalent static loads and its application

Otimização Paramétrica De Estruturas Treliçadas Sob a Ação De Cargas Dinâmicas Utilizando O Método Do Carregamento Estático Equivalente

High Fidelity and Efficient Computations of Dynamic Loads for Multidisciplinary Design Optimization of Flexible Transport Aircraft

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