Development of geometric algorithms in architectural planning and architectural structures

建筑规划和建筑结构中几何算法的开发

基本信息

批准号：
10205214
负责人：
KATOH Naoki
金额：
$ 6.72万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas (B)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

The results obtained are summarized as follows.1. We consider the problem of generating triangular meshes for planar regions and a class of curved surfaces using Steiner points that minimizes the maximum edge length ratio under the constraint that (1) the number of Steiner points are given or (2) the lower bound on minimum edge length is given. We have developed algorithms for the problem.2. Truss topology optimization problem for specified fundamental frequency has been shown to be formulated as SemiDefinite Programming (SDP) problem. An optimal topology with five-fold fundamental frequencies has been obtained without any difficulty. General forms of necessary and sufficient optimality conditions have been derived from the optimality conditions of the SDP problem, and the symmetry properties of optimal topologies have been investigated. It has also been shown that optimal solutions under linear buckling constraints can be found by successively applying SDP.3. Large-deformation analysis problem of cable networks has been formulated as Second-Order Cone Programming (SOCP) problem. It has been demonstrated that equilibrium shapes can be found without any even for an unstable equilibrium state.4. The design of room layout is determined by the adjacency of room, room size, shape, orientation and etc. We formulated the problem of optimal room layout as a mathematical programming problem from the viewpoint of geometric optimization. We have developed a new algorithm for the problem using orthogonal graph drawing algorithms.

获得的结果总结如下1。我们考虑使用施泰纳点为平面区域生成三角形网格和一类弯曲表面的问题，该点在（1）施用施泰纳点的最大边缘长度比最小化或（2）最小值的下限为（2）给出边缘长度。我们已经为问题开发了算法2。针对指定基本频率的桁架拓扑优化问题已被证明被表达为半决赛编程（SDP）问题。在没有任何困难的情况下获得了具有五倍基本频率的最佳拓扑。必要和充分的最佳条件的一般形式是从SDP问题的最佳条件中得出的，并且已经研究了最佳拓扑的对称性。还已经显示，可以连续应用SDP.3找到线性屈曲约束下的最佳解决方案。有线网络的大型信息分析问题已被提出为二阶圆锥编程（SOCP）问题。已经证明，即使对于不稳定的平衡状态，也没有任何平衡形状。4。房间布局的设计取决于房间，房间大小，形状，方向以及等等。我们从几何优化的角度来制定了最佳房间布局作为数学编程问题的问题。我们已经使用正交图形算法开发了一种用于问题的新算法。