Abstract
Shape optimization is a method to find the optimal shape of a structure by minimizing the objective function, i.e., volume and/or compliance under the design and limit constraints. The boundary of the structure is discretized using B-splines which allow local control and these control points are taken as design variables for the optimization formulation. The scaled boundary finite element method (SBFEM) is a semi-analytical approach, which has the combined advantage of both finite element method and the boundary element method. The SBFEM discretizes the boundary of the element, which reduces the computational domain size by one. Both the B-splines and the SBFEM discretizes the boundary of the structure, so the control points of the B-spline and the nodes of the SBFEM discretization can coincide to form the design variables. In this paper, we design a cantilever beam by using the shape optimization with the B-splines and the SBFEM. The cantilever beam is designed for minimum volume under a UDL and a point load with displacement constraint. The results obtained by the FEM and the SBFEM are compared.
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Kumar, K.E.S., Sundaramoothy, A., Natarajan, S., Rakshit, S. (2020). Shape Optimization of Beams with Scaled Boundary Finite Element Method and B-Splines. In: Salagame, R., Ramu, P., Narayanaswamy, I., Saxena, D. (eds) Advances in Multidisciplinary Analysis and Optimization. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-5432-2_18
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DOI: https://doi.org/10.1007/978-981-15-5432-2_18
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