请给出Craig-Bampton方法在MATLAB中的实现程序代码
时间: 2024-02-06 21:11:26 浏览: 176
CRC码MATLAB实现
很抱歉,由于Craig-Bampton方法涉及到具体的有限元模型和计算方法,其实现代码可能会比较复杂和具体化。因此,我无法直接提供完整的程序代码。
不过,下面是Craig-Bampton方法的MATLAB实现的一些常见步骤和代码示例,供您参考:
1. 定义有限元模型,并将其分解为多个子系统。可以使用MATLAB中的有限元分析工具箱(FEA Toolbox)来定义和分解有限元模型。
```
% 定义有限元模型
model = createpde('structural','static-solid');
% 定义材料和几何信息
E = 2e11; % 弹性模量
nu = 0.3; % 泊松比
thickness = 0.01; % 厚度
geometryFromEdges(model,@myedges);
structuralProperties(model,'YoungsModulus',E,'PoissonsRatio',nu,'Thickness',thickness);
% 网格划分和分解
generateMesh(model);
[~,nodes,elements] = findNodes(model);
nodeCount = size(nodes,2);
elementCount = size(elements,2);
numSubs = 5; % 分解成5个子系统
elementPerSub = ceil(elementCount/numSubs);
subNodes = nodes;
subElements = elements;
for i = 1:numSubs
startIndex = (i-1)*elementPerSub+1;
endIndex = min(i*elementPerSub,elementCount);
subElements(:,startIndex:endIndex) = 0;
for j = startIndex:endIndex
subElements(subElements == j) = j-startIndex+1;
end
end
```
2. 提取每个子系统的自由度矩阵,并计算其模态坐标。可以使用MATLAB中的有限元分析工具箱和模态分析工具箱来提取自由度矩阵和计算模态坐标。
```
% 提取子系统自由度矩阵
for i = 1:numSubs
subModel = createpde('structural','static-solid');
subNodes = nodes;
subElements = elements(:,(i-1)*elementPerSub+1:min(i*elementPerSub,elementCount));
subModel.Geometry.Nodes = subNodes';
subModel.Geometry.Elements = subElements';
subModel.Mesh.Nodes = subNodes';
subModel.Mesh.Elements = subElements';
generateMesh(subModel);
[~,subNodes,subElements] = findNodes(subModel);
subDOF = 3*size(subNodes,2);
subF = zeros(subDOF,1);
subModel.BoundaryConditions = structuralBC(subModel,'Face',1,'Displacement',[0,0,0]);
subStructuralProperties(subModel,'YoungsModulus',E,'PoissonsRatio',nu,'Thickness',thickness);
subStructuralProperties(subModel,'MassDensity',rho);
subStiffnessMatrix = assembleK(subModel);
subFEMesh = createFEMesh(subModel);
subDofList = subFEMesh.Nodes;
subDofList = subDofList(:);
subDofList = (subDofList-1)*3+1;
subK = subStiffnessMatrix(subDofList,subDofList);
subF = subF(subDofList);
subF = subF(subFEMesh.FreeNodes);
subU = subK\subF;
subUFull = zeros(subDOF,1);
subUFull(subDofList) = subU;
subDOFList{i} = subDofList;
subUList{i} = subUFull;
end
% 计算模态坐标
numModes = 30; % 计算前30个模态坐标
omegaList = zeros(numModes,1);
phiList = cell(numSubs,1);
for i = 1:numSubs
subU = subUList{i};
subK = subStiffnessMatrix(subDOFList{i},subDOFList{i});
subM = assembleM(subModel);
subM = subM(subDOFList{i},subDOFList{i});
[V,D] = eigs(subK,subM,numModes,'smallestabs');
omegaList = diag(D);
phiList{i} = V;
end
```
3. 将所有子系统的自由度矩阵和模态坐标组合为一个整体自由度矩阵和模态坐标。
```
% 组合所有子系统自由度矩阵和模态坐标
fullDOF = size(nodes,2)*3;
fullK = zeros(fullDOF,fullDOF);
fullPhi = zeros(fullDOF,numModes);
for i = 1:numSubs
subDofList = subDOFList{i};
subPhi = phiList{i};
for j = 1:length(subDofList)
for k = 1:length(subDofList)
fullK(subDofList(j),subDofList(k)) = fullK(subDofList(j),subDofList(k)) + subK(j,k);
end
for k = 1:numModes
fullPhi(subDofList(j),k) = fullPhi(subDofList(j),k) + subPhi(j,k);
end
end
end
```
4. 根据Craig-Bampton方法,将整体自由度矩阵和模态坐标缩减为一个小型模型。
```
% Craig-Bampton方法缩减
numCBModes = 10; % 缩减后保留前10个模态
cbDOFList = [1:6,fullDOF-5:fullDOF];
cbK = fullK(cbDOFList,cbDOFList);
cbPhi = fullPhi(cbDOFList,:);
cbPhiFull = zeros(fullDOF,numCBModes);
cbPhiFull(:,1:numCBModes) = cbPhi(:,1:numCBModes);
cbKReduced = cbPhiFull'*cbK*cbPhiFull;
cbMReduced = cbPhiFull'*fullM*cbPhiFull;
cbPhiReduced = cbPhiFull;
```
5. 对小型模型进行求解,得到系统的响应。
```
% 求解小型模型
cbFReduced = cbPhiFull'*fullF;
cbUReduced = cbKReduced\cbFReduced;
```
6. 根据小型模型的响应,反推出整个系统的响应。
```
% 反推出完整模型的响应
fullU = cbPhiFull*cbUReduced;
```
以上代码示例仅供参考,具体实现还需要根据具体的问题和要求进行适当的修改和调整。如果您有其他问题或疑问,欢迎继续提问。
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