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Implicit Heaviside filter with high continuity based on suitably graded THB splines

《机械工程前沿（英文）》 2022年第17卷第1期页码 14-14 doi: 10.1007/s11465-021-0670-2

摘要： The variable density topology optimization (TO) method has been applied to various engineering fields because it can effectively and efficiently generate the conceptual design for engineering structures. However, it suffers from the problem of low continuity resulting from the discreteness of both design variables and explicit Heaviside filter. In this paper, an implicit Heaviside filter with high continuity is introduced to generate black and white designs for TO where the design space is parameterized by suitably graded truncated hierarchical B-splines (THB). In this approach, the fixed analysis mesh of isogeometric analysis is decoupled from the design mesh, whose adaptivity is implemented by truncated hierarchical B-spline subjected to an admissible requirement. Through the intrinsic local support and high continuity of THB basis, an implicit adaptively adjusted Heaviside filter is obtained to remove the checkboard patterns and generate black and white designs. Threefold advantages are attained in the proposed filter: a) The connection between analysis mesh and adaptive design mesh is easily established compared with the traditional adaptive TO method using nodal density; b) the efficiency in updating design variables is remarkably improved than the traditional implicit sensitivity filter based on B-splines under successive global refinement; and c) the generated black and white designs are preliminarily compatible with current commercial computer aided design system. Several numerical examples are used to verify the effectiveness of the proposed implicit Heaviside filter in compliance and compliant mechanism as well as heat conduction TO problems.

关键词： topology optimization truncated hierarchical B-spline isogeometric analysis black and white designs Heaviside filter

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Meshless numerical method based on tensor product

SUN Haitao, WANG Yuanhan, MIAO Yu

《结构与土木工程前沿（英文）》 2008年第2卷第2期页码 166-171 doi: 10.1007/s11709-008-0021-y

摘要： A normalized space constructed by tensor product is used in field function approach to give a special case of moving least squares (MLS) interpolation scheme. In the regular domain, the field function which meets homogenous boundary conditions is constructed by spanning base space to make the MLS interpolation scheme simpler and more efficient. Owing to expanded basis functions selection, some drawbacks in general MLS method, for example repeated inversion, low calculation efficiency, and complex criterions, can be avoided completely. Numerical examples illustrate that the proposed method is characterized by simple mathematical concept, convenient repeat calculations with high accuracy, good continuity, less computation and rapid convergence.

关键词： mathematical continuity inversion selection efficient

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Principle and curve of planetary indexing cam mechanisms

LIU Ming-tao, ZHANG Ce, YANG Yu-hu

《机械工程前沿（英文）》 2006年第1卷第4期页码 475-478 doi: 10.1007/s11465-006-0063-6

摘要： A new type of planetary indexing cam mechanism called type !c is presented. The transmission principle of type !c is discussed. Based on the principle of formation of conjugate tooth contour, the equations of the cam s pitch curve are derived. The continuity and symmetry of the cam s pitch curve are also analyzed. It can be concluded that: 1) This type has no output institution so the output precision can be improved; 2) The asymmetrical two-ring structure is used to overcome dead point and its phase angle is equal to (π - 2π/n); 3) The continuous condition of the cam s pitch curve is that the average transmission ratio is -n in an intermittent motion period.

关键词： continuity planetary average transmission symmetry intermittent