Convergence Study of Local Continuum Sensitivity Method Using Spatial Gradient Reconstruction

Cross, David M.; Canfield, Robert A.

doi:10.2514/1.j053800

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…Numerous examples, conducted with Nastran analyses, demonstrated these attributes. The results also demonstrate that the method can be as accurate as other analytic DSA methods and more accurate than most [5].…”

mentioning

confidence: 73%

“…Spatial gradient reconstruction (SGR) was demonstrated as a means to improve CSA accuracy in a controllable and nonintrusive manner. Three journal articles [1][2][3] were published and four others [4][5][6][7] submitted for publication documenting the funded research. Seven conference papers were presented during the performance period [8][9][10][11][12][13][14].…”

Section: Discussionmentioning

confidence: 99%

“…In general, the convergence rate is largely dependent on the accuracy of the spatial derivative approximations that appear in the local CSE boundary conditions. The accuracy of these approximations is driven by the parameters used for the SGR [5].…”

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confidence: 99%

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Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Canfield¹

2014

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confidence: 73%

Section: Discussionmentioning

confidence: 99%

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Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Canfield¹

2014

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“…To obtain the spatial derivatives it is possible to apply the FDM or the Spatial Gradients Reconstruction (SGR). The latter technique was proposed by Cross and Canfield [17,39,40] and is based on the least-squares patch-recovery approach used by Duvigneau and Pelletier [41]. Being the domain one-dimensional, the two approaches can be applied indifferently.…”

Section: Csa Applicationmentioning

confidence: 99%

Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

Gagliardi,

Kulkarni,

Marulo

2024

Preprint

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Gradient-based optimization techniques need precise and efficient sensitivities. Numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods, such as the discrete and continuum ones are highly accurate and efficient. Continuum Sensitivity Analysis (CSA) is an analytical method used to calculate derivatives of shape or value parameters. While CSA has been successfully applied in static analysis and dynamic problems in the time domain, this work presents an extension of the approach to eigenvalue sensitivities for the first time. However, CSA revealed limitations, prompting the exploration of an alternative approach based on discrete analytical differentiation. This method is employed for the first time in shape sensitivities. The derivatives of the stiffness and mass matrices required by the method are calculated analytically, resulting in high accuracy and computational efficiency. In addition, an element-agnostic approach has been developed leveraging primary analysis matrices to calculate their derivative. This characteristic, along with the nonintrusivity, makes the method employable with standard commercial software. Both approaches have been applied and validated in a wide range of scenarios, involving vibration and buckling problems.

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“…2. The theoretical background and technical approach for SGR-based shape BV-CSA, documented in detail in references [10][11][12][13][14][15], is summarized next. Sample input data and their bulk data descriptions are shown in figures of the Appendix.…”

Section: Technical Approachmentioning

confidence: 99%

Shape Continuum Sensitivity Analysis using ASTROS and CAPS

Canfield

Durscher

Bryson

et al. 2019

AIAA Scitech 2019 Forum

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Continuum Sensitivity Analysis (CSA) is an analytic method that may compute derivatives with respective to shape variables, which may be formulated in fundamentally different ways. The boundary velocity formulation of CSA presented here enables an element-agnostic implementation that hinges upon post-processing of output from the analysis solver using a nonintrusive spatial gradient reconstruction (SGR) technique. SGR has been implemented as a module in the Automated Structural Optimization System (ASTROS). SGR provides the spatial derivatives used in conjunction with geometric sensitivity, also known as the design velocity, to form the convective term of CSA boundary conditions. The Computational Aircraft Prototype Syntheses (CAPS) program represents parametric associative geometry of solids and surfaces that conveniently provides the geometric sensitivity essential to forming the CSA boundary conditions. A procedure is described here that uses CAPS to provide the surface geometry, geometric sensitivity, and mesh of a finite element model for which ASTROS is used to perform SGR of the structural analysis output and then perform CSA. Results from a simple beam bending model in two-and three-dimensional space verify, against an analytic solution, the implementation of shape CSA using ASTROS and CAPS.

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Convergence Study of Local Continuum Sensitivity Method Using Spatial Gradient Reconstruction

Cited by 9 publications

References 23 publications

Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

Shape Continuum Sensitivity Analysis using ASTROS and CAPS

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