• Journal of Korean Association for Spatial Structures
• /
• v.12 no.1
• /
• pp.77-85
• /
• 2012

The membrane structure maintains stable form by giving initial tension to ductile membrane and increasing the stiffness of exterior that is much adopted in the large span spatial structure by making its thickness thin. This kind of membrane structure has characteristic that can express free-form curve, so the selection of structural form is very important. So, this paper proposes the expression of free-form surface based on NURBS basis function and the finite element method considering geometrical nonlinearity for the deduction of large deformation result. Also, for minimizing the approximation of the surface that is derived from the form-finding result, the interface method that change finite element mesh to NURBS is proposed. So, the optimum surface of free-form membrane is derived.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2008.04a
• /
• pp.216-221
• /
• 2008

Shape design optimization for linear elasticity problem is performed using isogeometric analysis method. In many design optimization problems for real engineering models, initial raw data usually comes from CAD modeler. Then designer should convert this CAD data into finite element mesh data because conventional design optimization tools are generally based on finite element analysis. During this conversion there is some numerical error due to a geometry approximation, which causes accuracy problems in not only response analysis but also design sensitivity analysis. As a remedy of this phenomenon, the isogeometric analysis method is one of the promising approaches of shape design optimization. The main idea of isogeometric analysis is that the basis functions used in analysis is exactly same as ones which represent the geometry, and this geometrically exact model can be used shape sensitivity analysis and design optimization as well. In shape design sensitivity point of view, precise shape sensitivity is very essential for gradient-based optimization. In conventional finite element based optimization, higher order information such as normal vector and curvature term is inaccurate or even missing due to the use of linear interpolation functions. On the other hands, B-spline basis functions have sufficient continuity and their derivatives are smooth enough. Therefore normal vector and curvature terms can be exactly evaluated, which eventually yields precise optimal shapes. In this article, isogeometric analysis method is utilized for the shape design optimization. By virtue of B-spline basis function, an exact geometry can be handled without finite element meshes. Moreover, initial CAD data are used throughout the optimization process, including response analysis, shape sensitivity analysis, design parameterization and shape optimization, without subsequent communication with CAD description.

• Steel and Composite Structures
• /
• v.37 no.6
• /
• pp.663-678
• /
• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.