• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1994.04a
• /
• pp.38-45
• /
• 1994

The general conceptual constitution of structural optimization is formulated. The algorithm using the gradient projection method and design sensitivity analysis is discussed. Examples of minimum-weight design for six-story steel plane frame are taken to illustrate the application of this algorithm. The advantages of this algorithm such as marginal cost and design sensitivity analysis as well as system analysis are explained.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.04a
• /
• pp.127-134
• /
• 2004

In this paper, using an adjoint variable method, we develop a design sensitivity analysis (DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume, respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.3% of CPU time far the finite differencing. Also, the topology optimization yields physical meaningful results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.12
• /
• pp.2631-2635
• /
• 2002

The semi-analytic sensitivity analysis using Pade approximation is presented for linear elastic structures. Although the semi-analytic method has several advantages, accuracy of the method prevents it from practical application. One of promising remedies is the use of geometric series for the matrix inversion. Though series expansion of order three has been successfully applied to the calculation of the structural sensitivity in the most range of the design perturbation, it is prone to have a slow convergence for large perturbation. To overcome this shortage, Pade approximation is introduced so that it can broaden the trust region of the perturbation without adding expansion terms. Numerical results show that the confident sensitivity can be obtained with tiny expenses of computation effort.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.05a
• /
• pp.90-95
• /
• 2001

A continuum-based shape design sensitivity analysis (DSA) method is presented for the acoustic radiation from thin body. The normal derivative integral formulation is employed as an analysis formulation and differentiated directly by using material derivative to get the acoustic shape design sensitivity. In the acoustic sensitivity formulation, derivative coefficients of the structural normal velocities on the surface are required as the input. Thus, the shape design sensitivities of structural velocities on the surface with respect to the shape change are also calculated with continuum approach. A simple disk is considered as a numerical example to validate the accuracy and efficiency of the analytical shape design sensitivity equations derived in this research. This research should be very helpful to design an application involving thin body and to change its acoustic characteristics.

• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.52 no.7
• /
• pp.307-314
• /
• 2003

This paper presents a 3D shape optimization algorithm for electromagnetic devices using the design sensitivity analysis with finite element method. The structural deformation analysis based on the deformation theory of the elastic body under stress is used for mesh renewing. The design sensitivity and adjoint variable formulae are derived for the 3D finite element method with edge element. The results of sensitivity analysis are used as the input data of the structural analysis to calculate the relocation of the nodal points. This method makes it possible that the new mesh of analysis region can be obtained from the initial mesh without regeneration. The proposed algorithm is applied to the shape optimization of 3D electromagnet pole to net a uniform flux density at the target region.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.101-108
• /
• 2000

An optimum design algorithm using efficient reanalysis is proposed for reliability-based optimization problems formulated as the minimization of initial cost and expected failure cost with reliability constraints. The reliability-based optimization is high cost to evaluate objective function and constraints needed reliability analysis. Therefore the sensitivity analysis of reliability index for approximated reanalysis is necessary. In this paper, three solution approaches are suggested and tested. The approaches include : (1) sensitivity analysis using finite difference; (2) sensitivity analysis using automatic differentiation (AD); and (3) sensitivity analysis with respect to intermediate variables using AD. Numerical example is optimized to show the reliability and effectiveness of the new algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2000.10a
• /
• pp.238-245
• /
• 2000

A general formulation for shape design sensitivity analysis over a plane arch structure is developed based on a variational formulation of curved beam in linear elasticity. Sensitivity formula is derived using the material derivative concept and adjoint variable method for the stress defined at a local segment. Obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation since it does not involve numerical differentiation. Due to the complete description for the shape and its variation of the arch, the formulation can manage more complex design problems with ease and gives better optimum design than before. Several examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems to illustrate the excellent applicability.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.10 no.3
• /
• pp.237-244
• /
• 2002

Analyzing acoustic-structural systems such as automobiles and aircraft, the FRF-based substructuring (FBS) method is one of the most powerful tools. In this paper, a general procedure for the parametric sensitivity analysis of vibro-acoustic problems has been presented using the multi-domain FRF-based substructuring formulation. For an acoustic-structural system sub-structured by multiple domains, the substructuring formulation gives the reaction farces on the interface boundaries. The design sensitivity formula is obtained from the direct differentiation of the reaction force expression with respect to the design vector. As a practical application, the proposed design sensitivity formula is applied to an engine mount system of passenger car. An objective of the problem is to identify the most effective engine mounts and bushes in minimizing the interior noise over the concerned rpm range. The comparison of the sensitivity results with those of the finite difference method shows excellent agreement. In addition, stiffness modifications of the mounts and bushes identified through the design sensitivity analysis lead to a successful decrease of the interior noise. This results show usefulness of the present method very well.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.3
• /
• pp.243-250
• /
• 2009

The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

• Journal of the Korea institute for structural maintenance and inspection
• /
• v.6 no.2
• /
• pp.183-194
• /
• 2002

A general procedure to evaluate the sensitivity of design variables to stresses and strains in PSC flexural members is proposed. To accomplish the purpose of this study, long-term losses including creep, shrinkage, and PS steel relaxation are formulated based on the equilibrium states of the deformed sectional geometry. Thereby, the formulation follows the basic steps which consider the fundamental formulas adopted by CEB-FIP, ACI, and KCI rather than the age adjusted effective modulus concept. Twenty-one design variable including the material and geometrical properties of concrete, nonprestressing steel and prestressing steel, and the geometry of the cross section are considered in the sensitivity analysis. The gradients of the stresses and strains needed for the sensitivity assessment are calculated in a closed format. The derived formulation is applied to the T-type section PSC beam with prestressing and nonprestressing steels for the sensitivity analysis. The analytically calculated sensitivity results are compared with those numerically calculated to ensure the validity of the proposed procedure.