A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems

Morse, Llewellyn; Khodaei, Zahra Sharif; Aliabadi, M.H.

doi:10.1016/j.enganabound.2019.05.021

Cited by 14 publications

(13 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For conciseness, the DBEM integral equations and their derivatives for plate bending are omitted. The DBEM integral equations for plate bending can be found in [10], while their derivatives with respect to some geometric parameter Z m can be found in [11].…”

Section: Methodology Dbem-based Idm For Plate Bending Problemsmentioning

confidence: 99%

“…The sensitivities of SIFs with the DBEM can be calculated numerically using the relatively crude Finite Difference Method (FDM), or analytically using the more efficient Implicit Differentiation Method (IDM) which involves deriving the derivatives of the DBEM fundamental solutions. To the knowledge of the authors, there is only one example of SIF sensitivities for plates being calculated with an IDM: Morse et al [11] derived the derivatives of the J-integral for plates to calculate SIF sensitivities for a plate with a centre crack subjected to complex loading conditions. Results were found to compare well with the FDM and the IDM was found to be significantly more efficient than the FDM.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

Morse¹,

Khodaei²,

Aliabadi³

2020

FRACTURE AND DAMAGE MECHANICS: Theory, Simulation and Experiment

Self Cite

View full text Add to dashboard Cite

A novel methodology is presented for the efficient reliability analysis of plate structures containing cracks with the Dual Boundary Element Method (DBEM). The derivatives of the DBEM plate formulations for the Crack Surface Displacement Extrapolation (CSDE) method have been derived for the first time and are used as part of an Implicit Differentiation Method (IDM) for the efficient calculation of Stress Intensity Factor (SIF) sensitivities. A numerical example is investigated in which results from the presented CSDE methodology are compared to those from the J-integral. The SIF sensitivities were used with the First-Order Reliability Method (FORM) to determine the reliability of a plate structure containing a crack. Results indicate that the proposed CSDE methodology is capable of providing estimates for reliability that are very similar to those provided by the J-integral. Given that the proposed CSDE methodology can be easier to implement, it could prove to be an effective alternative to the J-integral for the efficient reliability analysis of plate structures containing cracks.

show abstract

Section: Methodology Dbem-based Idm For Plate Bending Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

Morse¹,

Khodaei²,

Aliabadi³

2020

FRACTURE AND DAMAGE MECHANICS: Theory, Simulation and Experiment

Self Cite

View full text Add to dashboard Cite

show abstract

“…The first steps towards developing an IDM for plate or shell structures with the BEM were conducted by Morse et al in Reference 20, in which the exact/implicit derivatives of the BEM plate formulations with respect to geometrical variables were derived for the first time. These exact derivatives were only applicable to geometrical variables that influence the nodal coordinates of the BEM plate mesh, such as plate length or width, and so they were not applicable to geometrical variables that do not influence nodal coordinates, such as plate thickness.…”

Section: Introductionmentioning

confidence: 99%

“…Previous work by the research community involving exact⧵implicit derivatives of BEM formulations have focused on 2D structures, 1,3,[21][22][23][24][25][26][27][28] with some work conducted on 3D structures, 13,29 and one work so far on plate structures. 20 One notable example is Huang et al in which the implicit derivatives for the 2D dual boundary element method (DBEM), a version of BEM effective at modeling cracks, were developed for the first time and used to estimate the reliability of 2D structures using the First-Order Reliability Method (FORM). Another notable example is Brancati et al, 13 in which the implicit derivatives of 3D boundary element formulations were used to optimize noise levels in an aircraft cabin.…”

Section: Introductionmentioning

confidence: 99%

Manufacturing cost and reliability‐based shape optimization of plate structures

Morse

Mallardo

Aliabadi

2022

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

A novel methodology is presented for the manufacturing cost and reliability-based optimization of plate structures with the boundary element method (BEM), with the aim of improving the accuracy, robustness, and efficiency of the optimization of aircraft structures. The BEM plate formulations with respect to plate thickness are derived for the first time, and used as part of an implicit differentiation method (IDM), enabling the full shape optimization of plate structures with the BEM. These implicit derivatives are validated against derivatives obtained from the finite difference method (FDM) and from an analytical solution. Results indicate that the IDM is more robust than the FDM and in excellent agreement with the analytical solution, and more accurate than the FDM for most of the step-sizes investigated. To demonstrate the full shape optimization of plates with the newly developed IDM, a numerical example involving reliability-based design optimization and manufacturing cost optimization is presented for a plate structure. Results show that the newly developed IDM is more efficient than the FDM when performing this optimization.

show abstract

“…Based on the DBEM formulations for the generalized plane stress and Reissner plate bending theories, the static stress intensity factors for plates subjected to combined tension and bending loads have been estimated in Refs. [13,14].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Fracture Analysis of Plates Loaded in Tension and Bending Using the Dual Boundary Element Method

Khodaei

2019

KEM

Self Cite

View full text Add to dashboard Cite

The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements.

show abstract

A dual boundary element based implicit differentiation method for determining stress intensity factor sensitivities for plate bending problems

Cited by 14 publications

References 27 publications

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

Reliability-based fracture analysis for plate bending problems with the dual boundary element method

Manufacturing cost and reliability‐based shape optimization of plate structures

Dynamic Fracture Analysis of Plates Loaded in Tension and Bending Using the Dual Boundary Element Method

Contact Info

Product

Resources

About