Isogeometric design of elastic arches for maximum fundamental frequency

By A. Nagy, Mostafa Abdalla, Zafer Gürdal. 2011

59 citations recorded by the source corpus.

The isogeometric paradigm is aimed at unifying the geometric and analysis descriptions of engineering problems. This unification is brought about by employing the same basis functions describing the geometry to approximate the physical response. Non-uniform rational B-splines (NURBS) are commonly used for this purpose and are adopted in the present work for the design of elastic arches. Design for optimal shape and stiffness distribution is considered. Manufacturing constraints are imposed on shape and sizing variables. Shape changes are represented by altering spatial location of the control points and the associated weights. Sizing variables, that control the stiffness distribution, are defined at the control points and interpolated using the same spline basis functions. Since analysis, sizing, and shape design share the same underlying description, consistent discrete sensitivities can be easily evaluated analytically, greatly improving the performance of the optimisation process. While sizing should reflect the influence of local stress states, shape design is preferably performed at a global level. Thus, a multilevel approach is utilised, where shape design is carried out at a coarser level. Projecting the shape design sensitivities bridges the gap between the different levels. A variational formulation of essential manufacturing constraints for sizing and shape optimal design is introduced. The design framework is applied to fundamental frequency maximisation problems.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/8057c4a6e63f3dbc5ff0b4578363226913f99643

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Mechanical Engineering

Citations in the corpus

Isogeometric vibration analysis of free-form Timoshenko curved beams (2015, methodology): “[19] implemented the NURBS-based control mesh to find the optimal shape for the maximum natural frequency of Euler–Bernoulli curved beams.”
Shape optimization of continua using NURBS as basis functions (2013, methodology): “proposed a method using a shape change norm in shape optimization problems of elastic arches[30].”