Meshfree analysis and design sensitivity analysis for shell structures

Abstract

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.

Mixed functionals in the theory of nonlinearly elastic shells

“…These shortcomings are apparently because of the heuristic nature of such methods. This motivated researchers to develop meshfree, or meshless, methods [45,52,54] and mesh methods other than the FEM [2, 6, 7], approaches based on mixed variational principles [42,57,58], and finite-element models of low order [55,60].In the variational difference method (VDM) in the form of the finite-difference method (FDM), locking effects are less significant [2]. The authors of [2] point out that an attempt to satisfy, as accurately as possible, the additional conditions of functionals with the minimum number of varied parameters in the FEM adversely affects the accuracy of the stationarity conditions, while the reasonable inaccuracy of the former, as in the FDM and mixed FEM, produces more accurate trade-off schemes.…”

“…These shortcomings are apparently because of the heuristic nature of such methods. This motivated researchers to develop meshfree, or meshless, methods [45,52,54] and mesh methods other than the FEM [2, 6, 7], approaches based on mixed variational principles [42,57,58], and finite-element models of low order [55,60].…”

Isogeometric configuration design sensitivity analysis of finite deformation curved beam structures using Jaumann strain formulation

“…The discrete-analytical DSA method involves the analytical differentiation of discretized governing equation with respect to design variables. However, as mentioned in [1], since the finite element matrices are constructed using numerical integration, the explicit expression of finite element matrices in terms of design variables may not be available, and this discrete differentiation may not be achieved easily for general cases. Also, since the finite element matrix equation is an approximated one to the original continuum problem, it is theoretically dangerous to directly differentiate the finite element matrices [1].…”

A meshfree thin shell method for non‐linear dynamic fracture

“…However, the shell was developed for small deformations, small strains and elasticity. Three dimensional modelling of shear deformable shells and degenerated shells in a meshfree context was studied by Noguchi et al [2], Li et al [3] and Kim et al [4]. Usually, a low order polynomial basis was used, e.g.…”