Abstract
This paper presents an efficient and intuitive technique of shape parameterization for design optimization using a partial differential equation (PDE) of order ten. It shows how the choice of two introduced parameters can enable one to parameterize complex geometries. With the use of PDE based formulation, it is shown in this paper how the shape can be defined and manipulated on the basis of parameterization and the boundary value approaches by which complex shapes can be created. Further the boundary conditions which are used in it are a boundary and an intermediate curves for defining the shape. This technique allows complex shapes to be parameterized intuitively using a very small set of design parameters. Hence, Practical design optimization of problems becomes more achievable by applying PDE based approach of shape parameterization by incorporating standard numerical optimization techniques.
Highlights
Parameterizing the shape of objects is one of the essential factors in practical design optimization
The choice of parametric domain and boundary conditions pivot the shape of surface for acquiring solution of equation (1)
The final shape of the geometry can be manipulated by these boundary conditions as shown in figure 1
Summary
Parameterizing the shape of objects is one of the essential factors in practical design optimization. The aim of this paper is to optimize a parametric shape using minimum shape constraints based on 10th order partial differential equations (PDE) with 10 boundary conditions [7]. This technique follows a boundary-value approach where an object’s shape can consists of surface patches bounded by character curves. The choice of parametric domain and boundary conditions pivot the shape of surface for acquiring solution of equation (1). The final shape of the geometry can be manipulated by these boundary conditions as shown in figure 1. An insect bite may affects a particular part of the human skin which may cause that bitten part of skin to swell locally without tearing the whole skin; a shape can be optimized in the similar fashion
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