A Mindlin plate finite element with semi-analytical shape design sensitivities

Int. J. Numer. Meth. Engng

2004

SUMMARYAmong various sensitivity evaluation techniques, semi-analytical method (SAM) is quite popular since this method is more advantageous than analytical method (AM) and global finite difference method (GFD). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the pseudo load vector calculated by differentiation using the finite difference scheme. In the present study, an iterative refined semianalytical method (IRSAM) combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives. In eigenvalue problems, the tendency of eigenvalue sensitivity is similar to that of displacement sensitivity in static problems. Eigenvector is decomposed into rigid body mode and pure deformation mode. The present iterative SAM guarantees that the eigenvalue and eigenvector sensitivities converge to the reliable values for the wide range of perturbed size of the design variables. Accuracy and reliability of the shape design sensitivities in static problems and eigenvalue problems by the proposed method are assessed through the various numerical examples.

Section: Strip In Tension Problemmentioning

confidence: 99%

“…To improve accuracy in the range of the large perturbation size, it is required to consider the higher order terms. In the expansion of the higher order terms, the matrix inverse can be expressed by Von Neumann series [14].…”

Section: Introductionmentioning

confidence: 99%

A refined semi-analytic design sensitivity based on mode decomposition and Neumann series

Cho

Int. J. Numer. Meth. Engng

2004

“…Shell structures are frequently used in the construction of aerospace, automotive, and civil engineering structures. A significant amount of effort has been put into the design sensitivity analysis (DSA) and optimization of shell structures [1][2][3][4][5][6][7][8][9][10][11][12]. Yamazaki and Vandeplaats [3] performed sizing and shape DSA of isoparametric shell element using the discrete method.…”

Section: Introductionmentioning

confidence: 99%

Continuum‐based design sensitivity analysis and optimization of nonlinear shell structures using meshfree method

Choi

Numerical Meth Engineering

et al. 2006

SUMMARYA continuum-based shape and configuration design sensitivity analysis (DSA) method for a finite deformation elastoplastic shell structure has been developed. Shell elastoplasticity is treated using 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 the stress objectivity is preserved for finite rotation increments. The material derivative concept is used to develop a continuum-based shape and configuration DSA method. Significant computational efficiency is obtained by solving the design sensitivity equation without iteration at each converged load step using the same consistent tangent stiffness matrix. Numerical implementation of the proposed shape and configuration DSA is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples.

Meshfree analysis and design sensitivity analysis for shell structures

Numerical Meth Engineering

Choi

Chen

et al. 2002

SUMMARYA uniÿed design sensitivity analysis method for a meshfree shell structure with respect to size, shape, and conÿguration 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. Because of a strong connection to the CAD tool, the design variable is selected from the CAD parameters, and a consistent design velocity ÿeld is then computed by perturbing the surface geometric matrix. The material derivative concept is utilized in order to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and e ciency of the proposed design sensitivity analysis method compared to the analytical solution and the ÿnite di erence solution.