Multi-patch nonsingular isogeometric boundary element analysis in 3D

A multi-patch nonsingular isogeometric boundary element method (IGABEM) for 3D problems is presented that provides accurate solutions for multi-patch IGABEM. In order to conveniently implement this method, based on the Greville abscissae, a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches, and a simple method for merging equations handles the extra equations. The numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional IGABEM.

Acceleration of free-vibrations analysis with the Dual Reciprocity BEM based on ℋ-matrices and CUDA


– The purpose of this paper is to present a novel strategy used for acceleration of free-vibration analysis, in which the hierarchical matrices structure and Compute Unified Device Architecture (CUDA) platform is applied to improve the performance of the traditional dual reciprocity boundary element method (DRBEM).


– The DRBEM is applied in forming integral equation to reduce complexity. In the procedure of optimization computation, ℋ-Matrices are introduced by applying adaptive cross-approximation method. At the same time, this paper proposes a high-efficiency parallel algorithm using CUDA and the counterpart of the serial effective algorithm in ℋ-Matrices for inverse arithmetic operation.


– The analysis for free-vibration could achieve impressive time and space efficiency by introducing hierarchical matrices technique. Although the serial algorithm based on ℋ-Matrices could obtain fair performance for complex inversion operation, the CUDA parallel algorithm would further double the efficiency. Without much loss in accuracy according to the examination of the numerical example, the relative error appeared in approximation process can be fixed by increasing degrees of freedoms or introducing certain amount of internal points.


– The paper proposes a novel effective strategy to improve computational efficiency and decrease memory consumption of free-vibration problems. ℋ-Matrices structure and parallel operation based on CUDA are introduced in traditional DRBEM.

A CAD/CAE incorporate software framework using a unified representation architecture

Currently, there are still some big gaps between the CAD system and CAE system, e.g. the different data structure for model representation, which costs lots of time and effort of engineers in the interaction between these two kinds of systems. In order to bridge these gaps, an incorporate software framework is proposed in this paper. In this framework, the unified representation architecture (URA) is presented that makes CAD and CAE to be an organic entity. The URA contains three components: (1) unified data model (UDD) including unified B-rep, unified feature and unified mesh; (2) unified data management (UDM) consisting of unified interaction, unified data structure, unified Constructive Solid Geometry (CSG) history and unified interface; (3) unified display and post-processor (UDP) for both design and performance analysis. The URA facilitates the incorporation by explicitly representing design and analysis information as design features, which maintains their associations through the history chain. Besides the URA, a unified mesh data (UMD) is proposed to unify the mesh of CAD model display and CAE analysis with the purpose of reducing the redundancy of mesh data. The unified mesh data (UMD) is proposed to unify the mesh of CAD model display and CAE analysis, which greatly reduces the redundancy of mesh generation data. Finally, the high efficiency of the proposed framework is demonstrated by engineering examples.

Boundary condition related mixed boundary element and its application in FMBEM for 3D elastostatic problem

A boundary condition (BC) related mixed element method is presented to address the corner problem in boundary element method (BEM) for 3D elastostatic problems. In this method, noncontinuous elements (NCEs) are only used at the displacement-prescribed corners/edges and continuous elements (CEs) in other places, which can decrease the degrees of freedom (DOFs) compared to the approach using NCEs at all corners/edges. Moreover, an automatic generation algorithm of BC related mixed linear triangular elements is implemented with the help of 3D modeling engine ACIS, and the boundary element analysis (BEA) is integrated into CAD systems. In order to solve large scale problems, the fast multipole BEM (FMBEM) with mixed elements is proposed and utilized in the BEA. The examples show that the node shift scheme adopting 1/4 is optimal and the BEM/FMBEM using mixed elements can produce more accurate results by only increasing a small number of DOFs.

Topology optimization of total femur structure: application of parameterized level set method under geometric constraints

Optimization of the femur prosthesis is a key issue in femur replacement surgeries that provide a viable option for limb salvage rather than amputation. To overcome the drawback of the conventional techniques that do not support topology optimization of the prosthesis design, a parameterized level set method (LSM) topology optimization with arbitrary geometric constraints is presented. A predefined narrow band along the complex profile of the original femur is preserved by applying the contour method to construct the level set function, while the topology optimization is carried out inside the cavity. The Boolean R-function is adopted to combine the free boundary and geometric constraint level set functions to describe the composite level set function of the design domain. Based on the minimum compliance goal, three different designs of 2D femur prostheses subject to the target cavity fill ratios 34%, 54%, and 74%, respectively, are illustrated.

A novel approach for automatic reconstruction of boundary condition in structure analysis

Boundary conditions (BCs) are important parameters of numerical computation for CAE structure analysis. Automatically and correctly reconstructing BCs would evidently improve the design efficiency. In this pa- per, a novel approach consisting of feature representation of BCs, coding mechanism for BC related topo- logical entity and BC reconstructing mechanism is proposed. BCs treated as features can be adaptive to the changing geometric model in this approach. Coding mechanism guarantees that the specified entities of BCs from the model reconstruction process could be identified. Reconstructing mechanism comprises the maintenance of BC-geometry feature dependency, data consistency and coding transmission, which ensures all the BCs can be automatically updated in terms of the changing geometry. This approach can avoid repeatedly applying BCs to the whole or portion of topological entities. Finally, some representative cases demonstrate that the proposed approach is able to significantly improve the design efficiency.