def INCKE(KS, KEl):
#STIFF下位程序, 将单元刚度矩阵迭代插入总体刚度矩阵
mn = ref.arrIndexSort(KEl[0])[:,1].T
ij = ref.arrIndexSort(KEl[0])[:,0].T
KE = KEl[1]
map(lambda i: map(lambda j: AINCKE([[mn[i], mn[j]],KS], [[i,j],KE]), ij), ij)
return KS
def insKE(KS, lKE):
#GKS() sub reduce() function, insert KE of a single element
#lKE = [[[LableInElement, NodeLable],[0,91],[1,92], ...], KE]
mn = ref.arrIndexSort(lKE[0])[:,1].T
ij = ref.arrIndexSort(lKE[0])[:,0].T
KE = lKE[1]
map(lambda i: map(lambda j: insKEIJ([[mn[i], mn[j]],KS], [[i,j],KE]), ij), ij)
return KS
def INCKE(KS, KEl):
#STIFF下位程序, 将单元刚度矩阵迭代插入总体刚度矩阵
mn = ref.arrIndexSort(KEl[0])[:, 1].T
ij = ref.arrIndexSort(KEl[0])[:, 0].T
KE = KEl[1]
map(
lambda i: map(lambda j: AINCKE([[mn[i], mn[j]], KS], [[i, j], KE]), ij
), ij)
return KS
def insKE(KS, lKE):
#KS() sub reduce() function, insert KE of a single element
#lKE = [[[LableInElement, NodeLable],[0,91],[1,92], ...], KE]
mn = ref.arrIndexSort(lKE[0])[:, 1].T
ij = ref.arrIndexSort(lKE[0])[:, 0].T
KE = lKE[1]
map(
lambda i: map(lambda j: insKEIJ([[mn[i], mn[j]], KS], [[i, j], KE]), ij
), ij)
return KS
def FEM(inputDict):
#有限元
HIP = ref.arrIndexSort(inputDict['HIP'])
HIP = np.matrix(HIP[:,1:3].reshape(-1,1))
KS = STIFF(inputDict)
KS = INSCD(KS, inputDict['BIU'])
Solution = np.linalg.solve(KS, HIP)
Solution = np.array(Solution.reshape((-1,2)))
return Solution
def FEM(inputDict):
#有限元
HIP = ref.arrIndexSort(inputDict['HIP'])
HIP = np.matrix(HIP[:, 1:3].reshape(-1, 1))
KS = STIFF(inputDict)
KS = INSCD(KS, inputDict['BIU'])
Solution = np.linalg.solve(KS, HIP)
Solution = np.array(Solution.reshape((-1, 2)))
return Solution
def STIFF(FEMinput):
#生成总体刚度矩阵
IJMH = FEMinput['IJMH']
E = FEMinput['TEVW']['E']
PR = FEMinput['TEVW']['pr']
t = FEMinput['TEVW']['t']
XY = FEMinput['XY']
KS = np.zeros((FEMinput['XY'].shape[0]*2, FEMinput['XY'].shape[0]*2))
XY = ref.arrIndexSort(XY)
IJMH = ref.lstIndexSort(IJMH)
KEs = map(lambda EN: STE(XY[EN[1][:,1],:], E, PR, t, EN[0], IJMH), IJMH)#单元刚度矩阵List
KS = np.matrix(reduce(INCKE, KEs, KS))
return KS
def STIFF(FEMinput):
#生成总体刚度矩阵
IJMH = FEMinput['IJMH']
E = FEMinput['TEVW']['E']
PR = FEMinput['TEVW']['pr']
t = FEMinput['TEVW']['t']
XY = FEMinput['XY']
KS = np.zeros((FEMinput['XY'].shape[0] * 2, FEMinput['XY'].shape[0] * 2))
XY = ref.arrIndexSort(XY)
IJMH = ref.lstIndexSort(IJMH)
KEs = map(lambda EN: STE(XY[EN[1][:, 1], :], E, PR, t, EN[0], IJMH),
IJMH) #单元刚度矩阵List
KS = np.matrix(reduce(INCKE, KEs, KS))
return KS
def GKS(FEMinput):
#Calculate global stiffness matrix
IJ = FEMinput['IJ']
E = FEMinput['TEV']['E']
V = FEMinput['TEV']['V']
T = FEMinput['TEV']['T']
XY = FEMinput['XY']
KS = np.zeros((XY.shape[0]*2, XY.shape[0]*2))
XY = ref.arrIndexSort(XY)
IJ = ref.lstIndexSort(IJ)
KE = KEsquare(E, V, T)
KEsl = [KEdcr(KE, EN[0], IJ) for EN in IJ]#List of Element stiffness matrix
KS = np.matrix(reduce(insKE, KEsl, KS))
return KS
def GKS(FEMinput):
#Calculate global stiffness matrix
IJ = FEMinput['IJ']
E = FEMinput['TEV']['E']
V = FEMinput['TEV']['V']
T = FEMinput['TEV']['T']
XY = FEMinput['XY']
KS = np.zeros((XY.shape[0] * 2, XY.shape[0] * 2))
XY = ref.arrIndexSort(XY)
IJ = ref.lstIndexSort(IJ)
KE = KEsquare(E, V, T)
KEsl = [KEdcr(KE, EN[0], IJ)
for EN in IJ] #List of Element stiffness matrix
KS = np.matrix(reduce(insKE, KEsl, KS))
return KS
def INSCD(KS, BIU):
#插入支承条件, 修改总体刚度矩阵
BIU = ref.arrIndexSort(BIU)
KS = np.matrix(reduce(INSCDS, BIU, KS))
return KS
def INSCD(KS, BIU):
#插入支承条件, 修改总体刚度矩阵
BIU = ref.arrIndexSort(BIU)
KS = np.matrix(reduce(INSCDS, BIU, KS))
return KS