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Optimization of elastic systems using absolute nodal coordinate finite element formulation
Bojan Vohar, Marko Kegl, Zoran Ren, 2006, other scientific articles

Abstract: An approach to a shape optimization of elastic dynamic multibody systems is presented. The proposed method combines an appropriate shape parameterization concept and recently introduced finite element type using absolute nodal coordinate formulation (ANCF). In ANCF, slopes and displacements are used as the nodal coordinates instead of infinitesimal or finite rotations. This way one avoids interpolation of rotational coordinates and problems with finite rotations. ANCF elements are able to describe nonlinear deformation accurately; therefore, this method is very useful for simulations of lightweight multibody structures, where large deformations have to be taken into account. The optimization problem is formulated as a nonlinear programming problem and a gradient-based optimization procedure is implemented. The introduced optimization design variables are related to the cross-sectional parameters of the element and to the shape of the whole structure. The shape parameterization is based on the design element techniqueand a rational B ezier body is used as a design element. A body-like design element makes possible to unify the shape optimization of both simple beams and beam-like (skeletal) structures.
Keywords: mechanics, dynamics of material systems, multibody systems, elastic mechanical systems, manipulators, dynamically loaded beams, optimum shape design, absolute nodal coordinate formulation, design element technique, finite element method
Published in DKUM: 31.05.2012; Views: 2227; Downloads: 122
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Shape optimization of truss-stiffened shell structures with variable thickness
Marko Kegl, Boštjan Brank, 2006, original scientific article

Abstract: This paper presents an effective approach to shape optimal design of statically loaded elastic shell-like structures. The shape parametrization is based on a design element technique. The chosen design element is a rational Bézier body, enhanced with a smoothly varying scalar field. A body-like designelement makes possible to unify the shape optimization of both pure shells and truss-stiffened shell structures. The scalar field of the design element is obtained by attaching to each control point a scalar quantity, which is an add-on to the position and weight of the control point. This scalar field is linked to the shell thickness distribution, which can be optimized simultaneously with the shape of the shell. For linear and non-linear analysis of shell structures, a reliable 4-node shell finite element formulation is utilized. The presented optimization approach assumes the employment of a gradient-based optimization algorithm and the use of the discrete method of direct differentiation to perform the sensitivity analysis.Four numerical examples of shell and truss-stiffened shell optimization are presented in detail to illustrate the performance of the proposed approach.
Keywords: mechanics of structures, shape optimization, shells, trusses, Bézier body, numerical methods, optimum design
Published in DKUM: 30.05.2012; Views: 2136; Downloads: 120
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