Xiaoping Qian

Isogeometric analysis and shape optimization via boundary integral

In this paper, we present a boundary integral based approach to isogeometric analysis and shape optimization.For analysis, it uses the same basis, Non-Uniform Rational B-Spline (NURBS) basis, for both representing object boundary and for approximating physical fields in analysis via a Boundary-Integral-Equation Method (BIEM). We propose the use of boundary points corresponding to Greville abscissae as collocation points. We conducted h-, p- and k-refinement study for linear elasticity and heat conduction problems. Our numerical experiments show that collocation at Greville abscissae leads to overall better convergence and robustness. Replacing rational B-splines with the linear B-Splines as shape functions for approximating solution space in analysis does not yield significant difference in convergence.For shape optimization, it uses NURBS control points to parameterize the boundary shape. A gradient based optimization approach is adopted where analytical sensitivities of how control points affect objective and constraint functions are derived. Two 3D shape optimization examples are demonstrated.Our study finds that the boundary integral based isogeometric analysis and optimization have the following advantages: (1) the NURBS based boundary integral exhibits superior computational advantages over the usual Lagrange polynomials based BIEM on a per degree-of-freedom basis; (2) it bypasses the need for domain parameterization, a bottleneck in current NURBS based volumetric isogeometric analysis and shape optimization; (3) it offers tighter integration of CAD and analysis since both the geometric models for both analysis and optimization are the same NURBS geometry. Highlights? A NURBS based boundary integral method has been developed. ? It has superior computational advantages over traditional boundary integral. ? Greville collocation leads to accurate and stable analysis results. ? A boundary integral based isogeometric shape optimization method has been developed.

Design of heterogeneous turbine blade

Abstract Constantly rising operating pressure and temperature in turbine drivers push the material capabilities of turbine blades to the limit. The recent development of heterogeneous objects by layered manufacturing offers new potentials for the turbine blades. In heterogeneous turbine blades, multiple materials can be synthesized to provide better properties than any single material. A critical task of such synthesis in turbine blade design is an effective design method that allows a designer to design geometry and material composition simultaneously. This paper presents a new approach for turbine blade design, which ties B-spline representation of a turbine blade to a physics (diffusion) process. In this approach, designers can control both geometry and material composition. Meanwhile, material properties are directly conceivable to the designers during the design process. The designers role is enhanced from merely interpreting the optimization result to explicitly controlling both material composition and geometry according to the acquired experience (material property constraints). The mathematical formulation of the approach includes three steps: using B-spline to represent the turbine blade, using diffusion equation to generate material composition variation, using finite element method to solve the constrained diffusion equation. The implementation and examples are presented to validate the effectiveness of this approach for heterogeneous turbine blade design.

Feature-based design for heterogeneous objects

Abstract Heterogeneous objects are objects composed of different constituent materials. In these objects, multiple desirable properties from different constituent materials can be synthesized into one part. In order to obtain mass applications of such heterogeneous objects, efficient and effective design methodologies for heterogeneous objects are crucial. In this paper, we present a feature based design methodology to facilitate heterogeneous object design. Under this methodology, designers design heterogeneous objects using high-level design components that have engineering significance. These high level components are form features and material features. In this paper, we first examine the relationships between form features and material features in heterogeneous objects. We then propose three synthesized material features in accordance with our examination of these features. Based on these proposed features, we develop a feature based design methodology for heterogeneous objects. Two enabling methods for this design methodology, material heterogeneity specification within each feature and combination of these material features, are developed. A physics (diffusion) based B-spline method is developed to (1) allow design intent of material variation be explicitly captured by boundary conditions, (2) ensure smooth material variation across the feature volume. A novel method, direct face neighborhood alteration, is developed to increase the efficiency of combining heterogeneous material features. Examples of using this feature based design methodology for heterogeneous object design, such as a prosthesis design, are presented.

Direct Computing of Surface Curvatures for Point-Set Surfaces

Accurate computing of the curvatures of a surface from its discrete form is of fundamental importance for many graphics and engineering applications. The moving least-squares (MLS) surface from Levin [Lev2003] and its variants have been successfully used to define point-set surfaces in a variety of point cloud data based modeling and rendering applications. This paper presents a set of analytical equations for direct computing of surface curvatures from pointset surfaces based on the explicit definition from [AK04a, AK04b]. Besides the Gaussian parameter involved in the MLS definition, these analytical equations allow us to conduct direct and exact differential geometric analysis on the point-set surfaces without specifying any subjective parameters. Our experimental validation on both synthetic and real point cloud data demonstrates that such direct computing from analytical equations provides a viable approach for surface curvature evaluation for unorganized point cloud data.

A B-spline-based approach to heterogeneous objects design and analysis

The recent advancement of solid freeform fabrication, design techniques and fundamental understanding of material properties in functionally graded materials has made it possible to design and fabricate multifunctional heterogeneous objects. In this paper, we present an integrated design and analysis approach for heterogeneous object realization, which employs a unified design and analysis model based on B-spline representation and allows for direct interaction between the design and analysis model without laborious meshing operation. In the design module, a new approach for intuitively modelling of multi-material objects, termed heterogeneous lofting, is presented. In the analysis module, a novel graded B-spline finite element solution procedure is described, which gives orders of magnitude of better convergence rate in comparison with current methods, as demonstrated in several case studies. Further advantages of this approach include simplified mesh construction, exact geometry/material composition representation and easy extraction of an isomaterial surface for manufacturing process planning.

Recent Progress in Modeling, Simulation, and Optimization of Polymer Solar Cells

The power conversion efficiency of polymer solar cells today has passed 10%, the commonly acceptable value for commercial usage. However, in general labs, the power conversion efficiency routinely achievable is only at 3–5% because of the lack of effective tools to optimize the device design and the fabrication process. Instead of using trial-and-error experiments to improve the power efficiency, modeling and simulation provides an alternative, effective, and economical way to optimize the design of polymer solar cells for best device performance. This review gives a literature survey, including some of our own studies, on modeling and simulation of polymer solar cells. First, the fundamentals of polymer solar cells are briefly explained. Then, the optical and electrical modeling and simulation are discussed in detail, followed by a discussion on optimization of polymer solar cells via modeling and simulation. This review ends with an outlook for the future study on modeling, simulation, and optimization of polymer solar cells.

Blind estimation of general tip shape in AFM imaging

The use of flared tip and bi-directional servo control in some recent atomic force microscopes (AFM) has made it possible for these advanced AFMs to image structures of general shapes with undercut surfaces. AFM images are distorted representations of sample surfaces due to the dilation produced by the finite size of the tip. It is necessary to obtain the tip shape in order to correct such tip distortion. This paper presents a noise-tolerant approach that can for the first time estimate a general 3-dimensional (3D) tip shape from its scanned image in such AFMs. It extends an existing blind tip estimation method. With the samples, images, and tips described by dexels, a representation that can describe general 3D shapes, the new approach can estimate general tip shapes, including reentrant features such as undercut lines.

Adaptive Slicing of Moving Least Squares Surfaces: Toward Direct Manufacturing of Point Set Surfaces

Rapid advancement of 3D sensing techniques has led to dense and accurate point cloud of an object to be readily available. The growing use of such scanned point sets in product design, analysis, and manufacturing necessitates research on direct processing of point set surfaces. In this paper, we present an approach that enables the direct layered manufacturing of point set surfaces. This new approach is based on adaptive slicing of moving least squares (MLS) surfaces. Salient features of this new approach include the following: (I) It bypasses the laborious surface reconstruction and avoids model conversion induced accuracy loss. (2) The resulting layer thickness and layer contours are adaptive to local curvatures, and thus it leads to better surface quality and more efficient fabrication. (3) The curvatures are computed from a set of closed formula based on the MLS surface. The MLS surface naturally smoothes the point cloud and allows upsampling and downsampling, and thus it is robust even for noisy or sparse point sets. Experimental results on both synthetic and scanned point sets are presented.

Isogeometric analysis on triangulations

We present a method for isogeometric analysis on the triangulation of a domain bounded by NURBS curves. In this method, both the geometry and the physical field are represented by bivariate splines in Bernstein-Bezier form over the triangulation. We describe a set of procedures to construct a parametric domain and its triangulation from a given physical domain, construct C^r-smooth basis functions over the domain, and establish a rational Triangular Bezier Spline (rTBS) based geometric mapping that C^r-smoothly maps the parametric domain to the physical domain and exactly recovers the NURBS boundaries at the domain boundary. As a result, this approach can achieve automated meshing of objects with complex topologies and allow highly localized refinement. Isogeometric analysis of problems from linear elasticity and advection-diffusion analysis is demonstrated.

An optimization approach for constructing trivariate B-spline solids

In this paper, we present an approach that automatically constructs a trivariate tensor-product B-spline solid via a gradient-based optimization approach. Given six boundary B-spline surfaces for a solid, this approach finds the internal control points so that the resulting trivariate B-spline solid is valid in the sense the minimal Jacobian of the solid is positive. It further minimizes a volumetric functional to improve resulting parametrization quality. For a trivariate B-spline solid even with moderate shape complexity, direct optimization of the Jacobian of the B-spline solid is computationally prohibitive since it would involve thousands of design variables and hundreds of thousands of constraints. We developed several techniques to address this challenge. First, we develop initialization methods that can rapidly generate initial parametrization that are valid or near-valid. We then use a divide-and-conquer approach to partition the large optimization problem into a set of separable sub-problems. For each sub-problem, we group the B-spline coefficients of the Jacobian determinant into different blocks and make one constraint for each block of coefficients. This is achieved by taking an aggregate function, the Kreisselmeier-Steinhauser function value of the elements in each block. With block aggregation, it reduces the dimension of the problem dramatically. In order to further reduce the computing time at each iteration, a hierarchical optimization approach is used where the input boundary surfaces are coarsened to difference levels. We optimize the distribution of internal control points for the coarse representation first, then use the result as initial parametrization for optimization at the next level. The resulting parametrization can then be further optimized to improve the mesh quality. Optimized trivariate parametrization from various boundary surfaces and the corresponding parametrization metric are given to illustrate the effectiveness of the approach.