A triple acceleration method for topology optimization

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This paper presents a triple acceleration method (TAM) for the topology optimization (TO), which consists of three parts: multilevel mesh, initial-value-based preconditioned conjugate-gradient (PCG) method, and local-update strategy. The TAM accelerates TO in three aspects including reducing mesh scale, accelerating solving equations, and decreasing the number of updated elements. Three benchmark examples are presented to evaluate proposed method, and the result shows that the proposed TAM successfully reduces 35–80% computational time with faster convergence compared to the conventional TO while the consistent optimization results are obtained. Furthermore, the TAM is able to achieve a higher speedup for large-scale problems, especially for the 3D TOs, which demonstrates that the TAM is an effective method for accelerating large-scale TO problems.

Structural Design Optimization Using Isogeometric Analysis: A Comprehensive Review

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Isogeometric analysis (IGA), an approach that integrates CAE into conventional
CAD design tools, has been used in structural optimization for 10 years, with plenty of excellent
research results. This paper provides a comprehensive review on isogeometric shape
and topology optimization, with a brief coverage of size optimization. For isogeometric
shape optimization, attention is focused on the parametrization methods, mesh updating
schemes and shape sensitivity analyses. Some interesting observations, e.g. the popularity
of using direct (differential) method for shape sensitivity analysis and the possibility of developing
a large scale, seamlessly integrated analysis-design platform, are discussed in the
framework of isogeometric shape optimization. For isogeometric topology optimization
(ITO), we discuss different types of ITOs, e.g. ITO using SIMP (Solid Isotropic Material
with Penalization) method, ITO using level set method, ITO using moving morphable
com-ponents (MMC), ITO with phase field model, etc., their technical details and
applications such as the spline filter, multi-resolution approach, multi-material problems
and stress con-strained problems. In addition to the review in the last 10 years, the current
developmental trend of isogeometric structural optimization is discussed.

A multi-patch nonsingular isogeometric boundary element method using trimmed elements

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One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational B-spline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.

Multi-patch nonsingular isogeometric boundary element analysis in 3D

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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

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– 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

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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.