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Kyung K. Choi - One of the best experts on this subject based on the ideXlab platform.

  • Design Sensitivity Method for Sampling-Based RBDO With Varying Standard Deviation
    Journal of Mechanical Design, 2015
    Co-Authors: Hyunkyoo Cho, Kyung K. Choi, Ikjin Lee, David Lamb
    Abstract:

    Conventional reliability-based Design optimization (RBDO) uses the mean of input random variable as its Design variable; and the standard deviation (STD) of the random variable is a fixed constant. However, the constant STD may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is present as a percentage of the mean value. For this kind of Design problem, the STD of the input random variable should vary as the corresponding Design variable changes. In this paper, a method to calculate the Design Sensitivity of the probability of failure for RBDO with varying STD is developed. For sampling-based RBDO, which uses Monte Carlo simulation (MCS) for reliability analysis, the Design Sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STD in addition to the change in the mean. As copulas are used for the Design Sensitivity, correlated input random variables also can be used for RBDO with varying STD. Moreover, the Design Sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed Design Sensitivity method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate Design Sensitivity in the optimization process.

  • Design Sensitivity Method for Sampling-Based RBDO With Fixed COV
    Volume 2B: 41st Design Automation Conference, 2015
    Co-Authors: Hyunkyoo Cho, Kyung K. Choi, Ikjin Lee, David Lamb
    Abstract:

    Conventional reliability-based Design optimization (RBDO) uses the means of input random variables as its Design variables; and the standard deviations (STDEVs) of the random variables are fixed constants. However, the fixed STDEVs may not correctly represent certain RBDO problems well, especially when a specified tolerance of the input random variable is presented as a percentage of the mean value. For this kind of Design problem, the coefficients of variations (COVs) of the input random variables should be fixed, which means STDEVs are not fixed. In this paper, a method to calculate the Design Sensitivity of probability of failure for RBDO with fixed COV is developed. For sampling-based RBDO, which uses Monte Carlo simulation for reliability analysis, the Design Sensitivity of the probability of failure is derived using a first-order score function. The score function contains the effect of the change in the STDEV in addition to the change in the mean. As copulas are used for the Design Sensitivity, correlated input random variables also can be used for RBDO with fixed COV. Moreover, the Design Sensitivity can be calculated efficiently during the evaluation of the probability of failure. Using a mathematical example, the accuracy and efficiency of the developed method are verified. The RBDO result for mathematical and physical problems indicates that the developed method provides accurate Design Sensitivity in the optimization process.Copyright © 2015 by ASME

  • Continuum-Based Design Sensitivity Analysis and Optimization of Springback in Stamping Process
    Volume 2: 31st Design Automation Conference Parts A and B, 2005
    Co-Authors: Kyung K. Choi, Nam H. Kim, Mark E. Botkin
    Abstract:

    The springback is a significant manufacturing defect in the stamping process. A serious impediment to the use of lighter-weight, higher-strength materials in manufacturing is the relative lack of understanding about how these materials respond to the complex forming process. The springback problem can be reduced by using appropriate Designs of die, punch, and blank holder shape together with friction and blank holding force. That is, an optimum stamping process can be determined using a gradient-based optimization to minimize the springback. However, for an effective optimization of the stamping process, development of an efficient analytical Design Sensitivity analysis method is crucial. In this paper, a continuum-based shape and configuration Design Sensitivity analysis (DSA) method for the stamping process has been developed. The material derivative concept is used to develop the continuum-based Design Sensitivity. The Design Sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic nonlinear analysis with frictional contact, which makes the Design Sensitivity calculation very efficient. The accuracy and efficiency of the proposed method is illustrated by minimizing springback in an S-rail part, which is often used as an industrial benchmark to verify the numerical procedures employed for stamping processes.Copyright © 2005 by ASME

  • Energy flow analysis and Design Sensitivity of structural problems at high frequencies
    Journal of Sound and Vibration, 2003
    Co-Authors: Nam H. Kim, Jun Dong, Kyung K. Choi
    Abstract:

    The Design Sensitivity formulation of an energy finite element method is presented using the direct differentiation and adjoint variable methods. The continuum method is used to derive the Design Sensitivity equation of the energy flow equation, whereas the discrete method is used to calculate the variation of the coupling relation. For Design variables, material property, panel thickness, and structural shape are taken into account, in addition to the structural damping factor. The Design variable's effect on the power transfer coefficient is discussed in detail. Even if the system matrix equation is not symmetric, the adjoint problem is solved using the same factorized matrix from response analysis. Design Sensitivity results calculated from the proposed method are compared to the finite difference Sensitivity results with a good agreement.

  • Design Sensitivity Analysis of Nonlinear Shell Structure With Frictionless Contact
    Volume 2: 29th Design Automation Conference Parts A and B, 2003
    Co-Authors: Kyung K. Choi, Nam H. Kim, Mark E. Botkin
    Abstract:

    A continuum-based shape and configuration Design Sensitivity analysis method for a finite deformation elastoplastic shell structure with frictionless contact has been developed. Shell elastoplasticity is treated based on the projection method that performs the return mapping on the subspace defined by the zero-normal stress condition. An incrementally objective integration scheme is used in the context of finite deformation shell analysis, wherein stress objectivity is preserved for finite rotation increments. The penalty regularization method is used to approximate the contact variational inequality. The material derivative concept is used to develop continuum based Design Sensitivity. The Design Sensitivity equation is solved without iteration at each converged load step. Numerical implementation of the proposed shape and configuration Design Sensitivity analysis is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples.© 2003 ASME

Jasbir S. Arora - One of the best experts on this subject based on the ideXlab platform.

  • Design Sensitivity analysis in dynamic thermoviscoelasticity with implicit integration
    International Journal of Solids and Structures, 1996
    Co-Authors: Michael J. Poldneff, Jasbir S. Arora
    Abstract:

    Design Sensitivity equations for coupled thermoviscoelastic systems are discretized via the finite element method. The approach is developed for structural systems by using the total Lagrangian approach and the reference domain concept. The discretization is based on implicit integration schemes. The implementation of finite element and Design Sensitivity analysis utilizes the Christensen-Naghdi free energy function and the direct differentiation approach, which is most suitable for the systems under consideration. A relationship between the discretized Sensitivity equations and the equations for the original analysis is shown. Use of the same discretization for analysis and Sensitivity analysis is emphasized. Partial derivatives of the right-hand side required for Sensitivity calculations are implemented via the central difference method, which provides greater flexibility without sacrificing accuracy. Examples of analysis and Design Sensitivity analysis for a thermoviscoelastic non-linear truss and a plate with a hole are given. The calculated Sensitivity results are verified by comparison with overall finite difference calculations.

  • Structural Design Sensitivity Analysis: Continuum and Discrete Approaches
    Advances in Structural Optimization, 1995
    Co-Authors: Jasbir S. Arora
    Abstract:

    A unified approach for structural Design Sensitivity analysis involving both shape and sizing variables is presented. Starting with a continuum formulation and a general response functional needing Sensitivity analysis, the direct variation and adjoint approaches are derived. Discretization of the continuum expressions for the two approaches is presented and the numerical implementation aspects are discussed. The discretized forms of the continuum Sensitivity expressions are compared with the ones obtained by starting with the discretized model ab initio. This comparison shows that the two approaches give similar discretized expressions for numerical calculations. Therefore, exactly same procedures can be used for computer implementation of both the approaches. The continuum approach, however, gives certain insights that would not be possible with only the discrete approach. The presented analyses and insights lead to a unified view point for numerical implementation of Design Sensitivity analysis which is quite straightforward with existing or new finite element analysis codes. The explicit Design variations (partial derivatives with respect to the Design variables) of the internal and external nodal forces are the major calculations needed to implement the Design Sensitivity analysis. An implementation scheme is suggested that is quite general and simple needing minimal programming.

  • Design Sensitivity analysis for dynamic thermoviscoelastic problems
    5th Symposium on Multidisciplinary Analysis and Optimization, 1994
    Co-Authors: Michael J. Poldneff, Jasbir S. Arora
    Abstract:

    Design Sensitivity equations for coupled thermoviscoelastic systems are discretized via finite element method. The approach is developed for structural systems using the total Lagrangian approach and the reference domain concept. The temporal discretization is based on the implicit integration schemes. The implementation of finite element and Design Sensitivity analysis utilizes the ChristensenNaghdi free energy function and the direct differentiation approach which is most suitable for the systems under consideration. A relationship between the discretized Sensitivity equations and the equations for the original analysis is shown. Partial derivatives of the right hand side required for Sensitivity calculations are implemented via the central difference method which provides greater flexibility without sacrificing accuracy. Example of analysis and Design Sensitivity analysis for a thermoviscoelastic nonlinear truss is given. The calculated Sensitivity results are verified by comparison with overall finite difference calculations.

  • Design Sensitivity analysis of elastoplastic structures
    International Journal for Numerical Methods in Engineering, 1994
    Co-Authors: Makoto Ohsaki, Jasbir S. Arora
    Abstract:

    An iterative and incremental algorithm is presented for the Design Sensitivity Analysis (DSA) of elastoplastic structures. Geometrical non-linearity is included in the formulation, and the structure may be subjected to a cyclic loading. The key concept is discussed using an elastoplastic truss. It is shown that the Design Sensitivity Coefficients (DSCs) are path-dependent and discontinuous at the time at which yielding takes place in a member (yield time). In the proposed algorithm, the yield time is considered to be a function of the Design variables. In this way, the discontinuity in the DSCs at the material transition points can be overcome in a simple and routine way. Incremental response analysis and DSA are carried out simultaneously using the Newton–Raphson type iterative procedure. Since the proposed algorithm is completely consistent with the analysis procedure, it can be implemented into an existing code for structural analysis. Application to distributed parameter structures with kinematic and/or isotropic hardening is discussed using the von Mises yield condition and the elastic-predictor radial-return method. DSA is carried out for a ten-bar truss with a piecewise linear constitutive relation. It is shown that the DSCs found using the proposed method agree quite well with those calculated by the central difference method. Finally, an alternate method without any iteration for DSA is proposed and the results from the two methods are compared.

  • Design Sensitivity analysis of coupled thermoviscoelastic systems
    International Journal of Solids and Structures, 1993
    Co-Authors: Michael J. Poldneff, Jasbir S. Arora
    Abstract:

    Abstract Both the direct differentiation and adjoint variable methods for Design Sensitivity analysis of transient dynamic, arbitrarily nonlinear thermoviscoelastic coupled systems are presented in this paper. The approach is based on the thermodynamic description of simple materials due to Coleman. Large strains as well as arbitrary material nonlinearities are accounted for in the derivations. The domain parametrization or reference volume concept is used allowing a uniform treatment of both the shape and sizing Design Sensitivity analysis. Analytical examples demonstrating the use of the derived equations are given. This approach provides a solid basis for discretization of the developed equations for subsequent use in numerical computations.

Seonho Cho - One of the best experts on this subject based on the ideXlab platform.

  • Isogeometric Design Sensitivity analysis and experimental validation of nanoscale structures considering surface effects
    Structural and Multidisciplinary Optimization, 2018
    Co-Authors: Seung-ho Ahn, Bonyong Koo, Jae-hyun Kim, Seonho Cho
    Abstract:

    A continuum-based Design Sensitivity analysis (DSA) method is developed for nanoscale structures with surface effects. To account for the effects of precise geometry in the response and the Design Sensitivity analyses, we employ an isogeometric approach which uses the same NURBS basis functions as used to describe the geometry of CAD. A direct differentiation method is employed to obtain the analytical Design Sensitivity using a generalized Young-Laplace equation with high-order surface effects. Effective material properties with the surface effects for silver nanowires are measured from a three-point bending test using atomic force microscopy (AFM). The diameter and the suspended length of silver nanowires are considered as sizing and shape Design variables, respectively. The Design Sensitivity expressions are derived with respect to the Design parameters and validated comparing with the experimental results from the AFM scanning, showing an acceptable agreement.

  • Adjoint Design Sensitivity analysis of constant temperature molecular dynamics
    International Journal of Mechanics and Materials in Design, 2017
    Co-Authors: Hong-lae Jang, Seonho Cho
    Abstract:

    In this research, we proposed an efficient Design Sensitivity analysis (DSA) method for constant temperature molecular dynamics (MD). A Nose–Hoover thermostat is utilized to represent the possible state of a system that is in thermal equilibrium using a heat bath to maintain temperature constant. The Design Sensitivity of general performance measures is derived using an adjoint variable method. Since the adjoint system is path-dependent and derived in the form of a terminal value problem, the path of original MD analysis should be kept to be used with in the adjoint Sensitivity computation. The time reversibility of the MD system with Nose–Hoover thermostat is investigated. The accuracy and efficiency of the developed adjoint DSA method are verified through demonstrative numerical examples.

  • isogeometric shape Design Sensitivity analysis of elasticity problems using boundary integral equations
    Engineering Analysis With Boundary Elements, 2016
    Co-Authors: Minho Yoon, Seonho Cho
    Abstract:

    Abstract Using boundary integral equations and isogeometric approach, a shape Design Sensitivity analysis (DSA) method is developed for two dimensional elastic structures. In the isogeometric approach, NURBS basis functions in CAD systems are directly utilized in response analysis, which enables a seamless incorporation of exact geometry and higher continuity into computational framework. To enhance the accuracy of shape Design Sensitivity, the CAD-based higher-order geometric information such as curvature, normal, and tangential vector is exactly embedded in the Sensitivity expressions. In boundary integral formulation, shape Design velocity field is decomposed into normal and tangential components, which significantly affect the accuracy of shape Design Sensitivity. Also, the proposed boundary-based method does not require the tedious Design parameterization of internal domain. Through the numerical examples, the developed shape DSA method turns out to be more accurate than conventional finite element based one.

  • Adjoint Design Sensitivity analysis of molecular dynamics in parallel computing environment
    International Journal of Mechanics and Materials in Design, 2014
    Co-Authors: Hong-lae Jang, Jae-hyun Kim, Youmie Park, Seonho Cho
    Abstract:

    An adjoint Design Sensitivity analysis method is developed for molecular dynamics using a parallel computing scheme of spatial decomposition in both response and Design Sensitivity analyses to enhance the computational efficiency. Molecular dynamics is a path-dependent transient dynamic problem with many Design variables of high nonlinearity. Adjoint variable method is not appropriate for path-dependent problems but employed in this paper since the path is readily available from response analysis. The required adjoint system is derived as a terminal value problem. To compute the interaction forces between atoms in different spatial boxes, only atomic positions in the neighboring boxes are required to minimize the amount of data communications. Through some numerical examples, the high nonlinearity of the selected Design variables is discussed. Also, the accuracy of the derived adjoint Design Sensitivity is verified by comparing with finite difference Sensitivity and the efficiency of parallel adjoint variable method is demonstrated.

  • Efficient Design Sensitivity analysis of incompressible fluids using SPH projection method
    Structural and Multidisciplinary Optimization, 2009
    Co-Authors: Seonho Cho
    Abstract:

    Using the direct differentiation method, a Design Sensitivity analysis method for time-dependent incompressible fluids is developed. The fluid behavior is described as the motion of particles involved by the SPH method. In the SPH projection method, instead of changing the fluid density, incompressibility is enforced by the pressure Poisson equation derived from pressure projection, which enable to use larger time steps. In spite of the additional pressure Poisson equation, the computational cost for the Design Sensitivity is not expensive since the factorized system matrix of pressure Poisson equation can be utilized. Aforementioned computational efficiency is very beneficial for the Design Sensitivity computation required for every time step in explicit time integration and updated Lagrangian schemes, for which an update scheme of Design velocity field is developed using the velocity Sensitivity. Through demonstrative numerical examples, the developed DSA method turns out to be efficient and shows excellent agreement with finite differencing.

K.k. Choi - One of the best experts on this subject based on the ideXlab platform.

  • Design Sensitivity Analysis for the Meshfree Shell Structure
    Volume 2A: 27th Design Automation Conference, 2001
    Co-Authors: K.k. Choi, Nam H. Kim, Mark E. Botkin
    Abstract:

    Abstract A unified Design Sensitivity analysis method for a meshfree shell structure with respect to sizing, shape, and configuration Design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. The Design variable is selected from the CAD parameters, and a consistent Design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is used to obtain a Design Sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed Design Sensitivity analysis method compared to the analytical solution and the finite difference solution.

  • Shape Design Sensitivity analysis of nonlinear 2-D solids with elasto-plastic material
    Structural optimization, 1999
    Co-Authors: Y.-h. Park, K.k. Choi
    Abstract:

    A continuum-based shape Design Sensitivity analysis (DSA) method is presented for 2-D solid components with rate-independent elasto-plastic material. The material derivative of continuum mechanics is utilized to develop a continuum-based shape DSA method. The Design Sensitivity equation is derived using the incremental form of the equilibrium equation and increments of the static response with respect to shape Design variables. The direct differentiation method is utilized to obtain the first-order variation of the performance measure explicitly in terms of variations of shape Design variables. With the consistent tangent stiffness matrix employed at the end of each load step to compute the Design Sensitivity, the method does not require iterations to compute the Design Sensitivity. Numerical results are presented for a hollow cylinder model and a membrane with a hole model to validate the proposed DSA method.

  • Design Sensitivity Analysis of Truss Structures with Elastoplastic Material
    Mechanics of Structures and Machines, 1996
    Co-Authors: Y.-h. Park, K.k. Choi
    Abstract:

    ABSTRACT A continuum-based Design Sensitivity analysis (DSA) method is presented for configuration (or layout) Design of nonlinear structural systems with rate-independent elastoplastic material. Configuration Design variables are characterized by shape and orientation changes of the structural component. A continuum-based shape DSA method that utilizes the material derivative of continuum mechanics is extended to account for effects of shape and orientation variations. The incremental analysis method, with updated Lagrangian formulation, is used to derive the Design Sensitivity for the nonlinear structural system. To derive the Design Sensitivity, incremental energy and load forms are utilized. The first variations of energy and load forms and the static response with respect to configuration Design variables are described using the material derivative. Direct differentiation is utilized to obtain the first variation of the performance measure explicitly in terms of variations of configuration Design var...

  • Continuum approach for second-order shape Design Sensitivity of three-dimensional elastic solids
    AIAA Journal, 1994
    Co-Authors: Chin-jung Chen, K.k. Choi
    Abstract:

    A second-order shape Design Sensitivity analysis method for three-dimensional linear elastic solids is derived, using a continuum approach with the material derivative. To compute the second-order shape Design Sensitivity, a shape Design acceleration field is defined, which is similar to the shape Design velocity field for the first-order shape Design Sensitivity. Both direct differentiation and hybrid methods are presented in this paper. The shape changes are assumed on the traction-free boundary only. A numerical method, which can be implemented using established finite element analysis codes, is developed to demonstrate feasibility and accuracy of the proposed second-order shape Design Sensitivity analysis method

  • Configuration Design Sensitivity analysis of built-up structures part II: Numerical method
    International Journal for Numerical Methods in Engineering, 1993
    Co-Authors: Sung-ling Twu, K.k. Choi
    Abstract:

    A numerical method is presented for structural configuration Design Sensitivity calculations using established finite element analysis codes. The theoretical foundation of the configuration Design Sensitivity analysis is given in Part I of this paper1 using the continuum elasticity formulation. A linear approximation between Design parameterizations and Design velocity fields is derived for line and surface Design components. A regular Design velocity that avoids the calculation of corner terms at the boundary is implemented to show a unified configuration Design Sensitivity analysis. The Design Sensitivity analysis method is demonstrated using the post-processing data of an existing finite element code. Configuration Design Sensitivity results of displacement, stress and eigenvalue performance measures are illustrated for several built-up engineering structures.

Zhiye Zhao - One of the best experts on this subject based on the ideXlab platform.

  • Design Sensitivity analysis with hypersingular boundary elements
    Engineering Analysis with Boundary Elements, 2000
    Co-Authors: Zhiye Zhao, S.t. Lie
    Abstract:

    The finite difference load method for shape Design Sensitivity analysis requires the calculation of stress and stress gradient on the boundary. In the standard boundary element method, the basic state variables-displacement and traction are continuous, and are considered as very accurate. However, the boundary stress and stress gradient, derived from the differentiation of the state variables and Hooke's law, are discontinuous and have relatively lower accuracy than the basic state variables. The hypersingular boundary integral equation is introduced in this paper to determine the stress and stress gradient in the Design Sensitivity analysis. The numerical examples demonstrate the accuracy of the Design Sensitivity using the hypersingular boundary elements.

  • Shape Design Sensitivity analysis of kinematical boundaries
    Structural Optimization, 1993
    Co-Authors: Zhiye Zhao
    Abstract:

    A new approach is used in this paper to derive the Design Sensitivity formulation with kinematical Design boundaries. By employing the concept of the conventional finite difference approach, the variation of structural response due to change of the kinematic Design boundary can be represented by the perturbed structure under a set of kinematical boundary conditions. Parameterization of the Design variation with respect to the Design variable enables us to transform the Design Sensitivity into the solutions of a boundary value problem with perturbation displacements on the Design boundary. The perturbation diplacements can be evaluated from the stress and displacement fields of the initial problem. This approach can be treated as a special case of the general direct formulation, but the derivation using the finite difference procedure gives a strong physical meaning of the method, and the formulation derived provides an explicit form for Design Sensitivity calculation. The numerical implementation of this approach based on the boundary element method is discussed, and a few numerical examples are used to verify the proposed formulation.

  • An alternative approach to shape Design Sensitivity analysis
    International Journal for Numerical Methods in Engineering, 1992
    Co-Authors: Zhiye Zhao, R. A. Adey
    Abstract:

    A novel method is presented in this paper for calculating shape Design Sensitivity, which is based on the finite difference method (FDM). By analysing the numerical procedure of the FDM, the perturbation of the geometry is replaced by a perturbation load which can be calculated once the stress field of the initial problem and the Design boundary perturbation are known. The final shape Design Sensitivity is obtained by solving the perturbation problem which has the same geometry and the kinematical boundary condition as the initial problem, but under the perturbation loads. Therefore the new method does not require the calculation of the matrices of the perturbed structure, and is independent of the perturbation step. A numerical implementation of the finite difference load method (FDLM) is described in which the boundary element method is used to evaluate the structural response. The numerical examples demonstrate that this new method for shape Design Sensitivity analysis is very accurate.

  • Shape Design Sensitivity Analysis using the Boundary Element Method
    Lecture Notes in Engineering, 1991
    Co-Authors: Zhiye Zhao
    Abstract:

    The mathematical programming (MP) methods for shape optimization are iterative methods, in which the Designs are modified successively until all the criteria are satisfied. A key issue during the Design modification is to predict how the response of the structure changes due to the shape change of the structure. This information is called shape Design Sensitivity, which is defined as the rates of change of structural responses with respect to the Design variables. It is essential to provide accurate Design Sensitivity information in order to use those MP methods discussed in Chapter 2.

  • A Modified Finite Difference Method to Shape Design Sensitivity Analysis
    Boundary Elements XIII, 1991
    Co-Authors: Zhiye Zhao
    Abstract:

    A new method is presented in this paper for the calculation of shape Design Sensitivity with kinematical Design boundary. This new method modifies the traditional finite difference approach, such that the variation of the structural response due to the change of the kinematic boundary is replaced by an equivalent problem, and the final Design Sensitivity is expressed as the solutions of the initial structure under the perturbation displacements on the Design boundary. Two examples are used to demonstrate the proposed new formulation.