公开(公告)号：US08612186B2

公开(公告)日：2013-12-17

申请号：US13038330

申请日：2011-03-01

Applicant: Cheng-Tang Wu ,  Wei Hu

Inventor： Cheng-Tang Wu ,  Wei Hu

IPC: G06F17/50 ,  G06F7/60 ,  G06G7/48

CPC classification number: G06F17/5018

Abstract: System, method and software product for numerically simulating structural behaviors of an engineering product in compressible and near-incomprssible region is disclosed. Meshfree enriched finite element method (ME-FEM) is used for such numerical simulation. ME-FEM requires an engineering product be represented by a FEM model comprising a plurality of finite elements. Finite elements used in the ME-FEM are generally low-order finite elements. Each of the finite elements in the FEM model is enriched by at least one meshfree enriched (ME) node located within the element's domain. Each ME node has additional degrees-of-freedom for the element it belongs independent from those of the corner nodes. A displacement based first-order convex meshfree approximation is applied to the ME node. The convex meshfree approximation has Knonecker-delta property at the element's boundary. The gradient matrix of ME-FEM element satisfies integration constraint. ME-FEM interpolation is an element-wise meshfree interpolation that is discrete divergence-free at the incompressible limit.

Abstract translation: 公开了一种用于数值模拟工程产品在可压缩和近不可逆区域中的结构行为的系统，方法和软件产品。 无网格富集有限元法（ME-FEM）用于这种数值模拟。 ME-FEM要求工程产品由包括多个有限元素的FEM模型表示。 ME-FEM中使用的有限元素通常是低阶有限元。 FEM模型中的每个有限元素都由位于元素域内的至少一个无网格富集（ME）节点来丰富。 每个ME节点对于其所属的元件具有额外的自由度，独立于角点节点。 基于位移的一阶凸无网格近似被应用于ME节点。 凸无网格近似在元素边界处具有Knonecker-delta属性。 ME-FEM元素的梯度矩阵满足积分约束。 ME-FEM插值是在不可压缩极限处为离散无差异的元素无网格内插。

公开(公告)号：US07382367B1

公开(公告)日：2008-06-03

申请号：US11383135

申请日：2006-05-12

Applicant: Hongsheng Lu ,  Cheng-Tang Wu

Inventor： Hongsheng Lu ,  Cheng-Tang Wu

IPC: G06T17/20

CPC classification number: G06T17/20

Abstract: A method and system for transferring state variables between an old and new model in an adaptive mesh-free analysis is described. The old and the new model are associated with a set of old and new integration points, respectively. A third set of nodes is formed to include old boundary nodes and the set of old integration points. For each of the new integration points, a sub-set of the third set is defined. The support of each node of the sub-set covers the new integration point to be evaluated. A local interpolant with a desirable consistency condition and interpolation properties is constructed to interpolate state variables at the new integration points. All of the non-interpolated approximation can be transformed into the interpolated approximation with the desired consistency condition and smoothness using this procedure.

Abstract translation: 描述了一种在自适应网格分析中在旧模型和新模型之间传递状态变量的方法和系统。 旧的和新的模型分别与一组新的和新的集成点相关联。 形成第三组节点以包括旧边界节点和一组旧的积分点。 对于每个新的集成点，定义第三组的子集。 子集的每个节点的支持覆盖了要评估的新集成点。 构建具有期望的一致性条件和内插特性的局部内插器来在新的积分点处插值状态变量。 使用该过程，所有的非内插近似可以被转换成具有期望的一致性条件和平滑度的内插近似。

公开(公告)号：US07660480B1

公开(公告)日：2010-02-09

申请号：US11351794

申请日：2006-02-10

Applicant: Cheng-Tang Wu ,  Hongsheng Lu

Inventor： Cheng-Tang Wu ,  Hongsheng Lu

IPC: G06K9/40 ,  G06F7/60 ,  G06F17/10 ,  G06F9/45 ,  G06F9/455 ,  G06T15/00 ,  G06T17/00 ,  G06T15/30 ,  G06T17/20

CPC classification number: G06T17/20

Abstract: A two-level transformation scheme to enable a practical fast mesh-free method is disclosed. The first level transformation transforms the original chosen mesh-free shape function to a first transformed mesh-free shape function that preserves Kronecker delta properties. The first transformed mesh-free function allows the essential boundary conditions to be imposed directly. The second-level transformation scheme employs a low pass filter function served as a regularization process that filters out the higher-order terms in the monomial mesh-free approximation obtained from the first-level transformation scheme with desired consistency and completeness conditions. This integration scheme requires only a low-order integration rule comparing to the high order integration rule used in the traditional mesh-free methods. The present invention simplifies the boundary condition treatments and avoids the usage of high-order integration rule and therefore is more practical than the traditional mesh-free methods.

Abstract translation: 公开了一种实现快速无网格实用的方法的两级转换方案。 第一级变换将原始选择的无网格形状函数转换为保留Kronecker delta属性的第一个无变换网格形状函数。 第一个无网格变换功能允许直接施加基本边界条件。 第二级转换方案采用低通滤波器函数作为正则化过程，其过滤出从具有期望的一致性和完整性条件的第一级变换方案获得的单项无网格近似中的高阶项。 与传统的无网格方法中使用的高阶整合规则相比，该集成方案只需要一个低阶积分规则。 本发明简化了边界条件处理，避免了高阶整合规则的使用，因此比传统的无网格方法更为实用。

公开(公告)号：US08768660B2

公开(公告)日：2014-07-01

申请号：US13251654

申请日：2011-10-03

Applicant: Cheng-Tang Wu

Inventor： Cheng-Tang Wu

IPC: G06F7/60 ,  G06F17/10 ,  G06F17/50 ,  G06T17/20

CPC classification number: G06F17/5018 ,  G01N2203/0216 ,  G06F2217/16 ,  G06F2217/44 ,  G06T17/20

Abstract: Methods and systems for numerically simulating structural behaviors of embedded bi-materials are disclosed. At least first and second grid models are created independently for an embedded bi-material that contains an immersed material embedded entirely within a base material. First group of meshfree nodes represents the entire domain (i.e., base plus immersed materials). Second group of meshfree nodes represents the immersed or embedded material, which includes all interface nodes and nodes located within a space bordered by the material interface. Numerical structural behaviors of the embedded bi-material are simulated using the first and second set of meshfree nodes with a meshfree method that combines two meshfree approximations. The first meshfree approximation covers the first set of meshfree nodes and is based on properties of the base material, while the second meshfree approximation covers the second set of meshfree nodes and is based on a differential between the immersed and base materials.

Abstract translation: 公开了用于数值模拟嵌入式双材料结构行为的方法和系统。 至少第一和第二格栅模型是独立地为包含完全嵌入基材的浸入材料的嵌入式双材料而创建的。 第一组无网格节点表示整个域（即，基底加上浸没的材料）。 第二组无网节点代表浸没或嵌入的材料，其中包括位于物料界面边界的空间内的所有接口节点和节点。 嵌入式双材料的数值结构行为使用组合两个无网格近似的无网格方法，使用第一组和第二组无网格节点进行模拟。 第一个无网格近似覆盖第一组无网格节点，并且基于基础材料的性质，而第二无网格近似覆盖第二组无网格节点，并且基于浸没和基材之间的差异。

公开(公告)号：US20120226482A1

公开(公告)日：2012-09-06

申请号：US13038330

申请日：2011-03-01

Applicant: Cheng-Tang Wu ,  Wei Hu

Inventor： Cheng-Tang Wu ,  Wei Hu

IPC: G06F17/10

CPC classification number: G06F17/5018

Abstract: System, method and software product for numerically simulating structural behaviors of an engineering product in compressible and near-incomprssible region is disclosed. Meshfree enriched finite element method (ME-FEM) is used for such numerical simulation. ME-FEM requires an engineering product be represented by a FEM model comprising a plurality of finite elements. Finite elements used in the ME-FEM are generally low-order finite elements. Each of the finite elements in the FEM model is enriched by at least one meshfree enriched (ME) node located within the element's domain. Each ME node has additional degrees-of-freedom for the element it belongs independent from those of the corner nodes. A displacement based first-order convex meshfree approximation is applied to the ME node. The convex meshfree approximation has Knonecker-delta property at the element's boundary. The gradient matrix of ME-FEM element satisfies integration constraint. ME-FEM interpolation is an element-wise meshfree interpolation that is discrete divergence-free at the incompressible limit.

Abstract translation: 公开了一种用于数值模拟工程产品在可压缩和近不可逆区域中的结构行为的系统，方法和软件产品。 无网格富集有限元法（ME-FEM）用于这种数值模拟。 ME-FEM要求工程产品由包括多个有限元素的FEM模型表示。 ME-FEM中使用的有限元素通常是低阶有限元。 FEM模型中的每个有限元素都由位于元素域内的至少一个无网格富集（ME）节点来丰富。 每个ME节点对于其所属的元件具有额外的自由度，独立于角点节点。 基于位移的一阶凸无网格近似被应用于ME节点。 凸无网格近似在元素边界处具有Knonecker-delta属性。 ME-FEM元素的梯度矩阵满足积分约束。 ME-FEM插值是在不可压缩极限处为离散无差异的元素无网格内插。

公开(公告)号：US07702490B1

公开(公告)日：2010-04-20

申请号：US11113552

申请日：2005-04-25

Applicant: Cheng-Tang Wu ,  Yong Guo

Inventor： Cheng-Tang Wu ,  Yong Guo

IPC: G06F7/60 ,  G06F17/10 ,  G06G7/48

CPC classification number: G06F17/5018

Abstract: A method, system and computer program product pertained to adaptive discretization refinement of shell structure is disclosed. The adaptive mesh-free model is based on a technique for dividing the critical area into a finer model. The present invention is a method for enabling adaptive mesh-free shell structure in a time-domain analysis, the method comprises: defining the mesh-free shell structure by a structural geometry description file including a plurality of nodes and a reference 3-D mesh, which includes a plurality of shell elements, mapping the 3-D reference mesh into a 2-D parametric plane, wherein the 2-D parametric mesh includes a plurality of integration cells corresponding to the plurality of shell elements, solving structural responses at current solution cycle using mesh-free mathematical approximations pertaining to each of the plurality of integration cells, performing adaptive discretization refinement for the plurality of the integration cells.

Abstract translation: 披露了一种适用于离散化壳体结构的方法，系统和计算机程序产品。 自适应无网格模型基于将关键区域划分为更精细模型的技术。 本发明是一种在时域分析中实现自适应无网壳结构的方法，该方法包括：通过包括多个节点和参考3-D网格的结构几何描述文件来定义无网孔的壳结构 ，其包括多个壳单元，将所述3-D参考网格映射到2-D参数平面中，其中所述2-D参数网格包括对应于所述多个壳单元的多个积分单元，在当前解决结构响应 求解循环，使用与所述多个积分单元中的每一个相关联的无网格数学近似，对所述多个积分单元执行自适应离散化细化。

公开(公告)号：US07499050B2

公开(公告)日：2009-03-03

申请号：US10990003

申请日：2004-11-16

Applicant: Cheng-Tang Wu ,  Yong Guo

Inventor： Cheng-Tang Wu ,  Yong Guo

IPC: G06T17/00 ,  G06F7/60 ,  G06F17/10

CPC classification number: G06F17/5018

Abstract: A method, system and computer program product pertained to engineering analysis of a general three-dimensional (3-D) shell structure using the mesh-free technique is disclosed. The structural responses are solved with mesh-free technique after the 3-D shell structure is mapped to a two-dimensional plane. According to one aspect, the present invention is a method for mesh-free analysis of a general three-dimensional shell structure, the method comprises: defining the general shell structure as a physical domain represented by a plurality of nodes in a three-dimensional space, creating a plurality of projected nodes by mapping the plurality of nodes in the three-dimensional space onto a two-dimensional plane, assigning a plurality of domain of influences, one for each of the plurality of projected nodes, and calculating a solution of the physical domain using a set of mathematical approximations pertaining to each of the plurality of projected nodes.

Abstract translation: 公开了一种使用无网格技术对一般三维（3-D）壳结构进行工程分析的方法，系统和计算机程序产品。 在将三维壳结构映射到二维平面之后，结构响应由无网格技术解决。 一方面，本发明是一种一般三维壳结构的无网格分析方法，该方法包括：将一般壳结构定义为由三维空间中的多个节点表示的物理域 通过将所述三维空间中的所述多个节点映射到二维平面上来创建多个投影节点，分配多个影响域，所述多个影响域针对所述多个投影节点中的每一个，并且计算所述多个投影节点的解 物理域使用与多个投影节点中的每一个有关的一组数学近似。

公开(公告)号：US20130085727A1

公开(公告)日：2013-04-04

申请号：US13251654

申请日：2011-10-03

Applicant: Cheng-Tang Wu

Inventor： Cheng-Tang Wu

IPC: G06F17/10

CPC classification number: G06F17/5018 ,  G01N2203/0216 ,  G06F2217/16 ,  G06F2217/44 ,  G06T17/20

Abstract: Methods and systems for numerically simulating structural behaviors of embedded bi-materials are disclosed. At least first and second grid models are created independently for an embedded bi-material that contains an immersed material embedded entirely within a base material. First group of meshfree nodes represents the entire domain (i.e., base plus immersed materials). Second group of meshfree nodes represents the immersed or embedded material, which includes all interface nodes and nodes located within a space bordered by the material interface. Numerical structural behaviors of the embedded bi-material are simulated using the first and second set of meshfree nodes with a meshfree method that combines two meshfree approximations. The first meshfree approximation covers the first set of meshfree nodes and is based on properties of the base material, while the second meshfree approximation covers the second set of meshfree nodes and is based on a differential between the immersed and base materials.

Abstract translation: 公开了用于数值模拟嵌入式双材料结构行为的方法和系统。 至少第一和第二格栅模型是独立地为包含完全嵌入基材的浸入材料的嵌入式双材料而创建的。 第一组无网格节点表示整个域（即，基底加上浸没的材料）。 第二组无网节点代表浸没或嵌入的材料，其中包括位于物料界面边界的空间内的所有接口节点和节点。 嵌入式双材料的数值结构行为使用组合两个无网格近似的无网格方法，使用第一组和第二组无网格节点进行模拟。 第一个无网格近似覆盖第一组无网格节点，并且基于基础材料的性质，而第二无网格近似覆盖第二组无网格节点，并且基于浸没和基材之间的差异。

公开(公告)号：US20060103648A1

公开(公告)日：2006-05-18

申请号：US10990003

申请日：2004-11-16

Applicant: Cheng-Tang Wu ,  Yong Guo

Inventor： Cheng-Tang Wu ,  Yong Guo

IPC: G06T17/20 ,  G06T15/30

CPC classification number: G06F17/5018

Abstract: A method, system and computer program product pertained to engineering analysis of a general three-dimensional (3-D) shell structure using the mesh-free technique is disclosed. The structural responses are solved with mesh-free technique after the 3-D shell structure is mapped to a two-dimensional plane. According to one aspect, the present invention is a method for mesh-free analysis of a general three-dimensional shell structure, the method comprises: defining the general shell structure as a physical domain represented by a plurality of nodes in a three-dimensional space, creating a plurality of projected nodes by mapping the plurality of nodes in the three-dimensional space onto a two-dimensional plane, assigning a plurality of domain of influences, one for each of the plurality of projected nodes, and calculating a solution of the physical domain using a set of mathematical approximations pertaining to each of the plurality of projected nodes.