Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis

SUMMARYIn this paper, an error estimator that quantifies the effect of the finite element discretization error on the computation of the stress intensity factor in linear elastic fracture mechanics is presented. In order to obtain the proposed estimator, a shape design sensitivity analysis (SDSA) is applied to the fracture mechanics problem. Following this approach, one of the most efficient post-processing techniques for computing the strain energy release rate G, the well-known EDI method, may be interpreted as a continuum method of the SDSA. The proposed error estimator is based on the recovery of the gradient fields and its reliability has been checked by means of numerical problems, yielding very good estimations of the true error. The new estimator remarkably improves the results given by a previous error estimator, which is based on a discrete analytical approach of SDSA. As a consequence, the combination of the new error estimator and the result given by the EDI method provides a much more accurate estimation of G.

Section: Improvement Of G When Computed Through the Edi Methodmentioning

confidence: 74%

Section: Numerical Implementation Of the Continuum Approach Of Sdsa Imentioning

confidence: 96%

Section: Numerical Implementation Of the Continuum Approach Of Sdsa Imentioning

confidence: 99%

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An improvement of the EDI method in linear elastic fracture mechanics by means of an a posteriori error estimator in G

Giner

Fuenmayor

Tarancón

2003

“…The introduction of other kinds of errors during the SDSA, for example errors associated to a finite difference approximation, could distort the results of the analyses. Therefore, in this paper, the SDSA for the evaluation of m in Equation (6) has been carried out using the Discrete Analytical Approach [12,13] which does not introduce errors other than the discretization error.…”

Section: Methodology For Quality Assessment Of Shape Design Velocity mentioning

confidence: 99%

A numerical methodology to assess the quality of the design velocity field computation methods in shape sensitivity analysis

Ródenas

Fuenmayor

Tarancón

2004

A numerical methodology to assess the quality of the design velocity field computation methods in shape sensitivity analysis J. J. Ródenas * , † , F. J. Fuenmayor and J. E. Tarancón Departamento de Ingeniería Mecánica y de Materiales, Universidad Politécnica deValencia, E-46022 Valencia, Spain SUMMARYThe velocity field in shape sensitivity analysis is not uniquely defined although it must meet numerous theoretical and practical criteria. These practical criteria can be used to compare the existing velocity field computation methods which meet the theoretical criteria, but only in qualitative terms. When the FEM is used in design sensitivity analysis (DSA), due to the FE discretization error, the DSA errors will depend on the design velocity field considered. This paper presents a numerical methodology for quality evaluation of design velocity field computation methods in quantitative terms based on the analysis of the DSA discretization error.The sensitivity of the squared energy norm ( m = * u 2 /*a m , a m being a design variable) has been taken as the magnitude to measure the error of the DSA. For h-refinements, the squared error in energy norm ( e(u) 2 ) and the error in m (e( m )) are theoretically related by a constant which is independent of the refinement degree of the FE model. The quality of the design velocity field computation methods can therefore be assessed in terms of the stability of e( m )/ e(u) 2 in sequences of meshes. An example of the use of this methodology, where six design velocity field computation methods are compared, is presented.

“…However, its formulation and implementation are more di cult and dependent on the particular ÿnite element type. This method has been successfully applied to isoparametric and truss elements [1][2][3], but its application to more complex elements can be very cumbersome, specially for non-linear structures.…”

Section: Introductionmentioning

confidence: 99%

Improvement of semi‐analytical design sensitivities of non‐linear structures using equilibrium relations

Parente

Vaz

2001

SUMMARYThe accuracy problem of the semi-analytical method for shape design sensitivity analysis has been reported for linear and non-linear structures. The source of error is the numerical di erentiation of the element internal force vector, which is inherent to the semi-analytical approach. Such errors occur for structures whose displacement ÿeld is characterized by large rigid body rotations of individual elements. This paper presents a method for the improvement of semi-analytical sensitivities. The method is based on the element free body equilibrium conditions, and on the exact di erentiation of the rigid body modes. The method is e cient, simple to code, and can be applied to linear and non-linear structures. The numerical examples show that this approach eliminates the abnormal errors that occur in the conventional semi-analytical method.