sympy_fe_utilities Namespace Reference

Functions
def	DefineMatrix (name, m, n)
	This method defines a symbolic matrix. More...
def	DefineSymmetricMatrix (name, m, n)
	This method defines a symbolic symmetric matrix. More...
def	DefineSymmetricFourthOrderTensor (name, m, n, o, p)
	This method defines a symbolic symmetric 4th order tensor. More...
def	DefineVector (name, m)
	This method defines a symbolic vector. More...
def	DefineShapeFunctions (nnodes, dim, impose_partion_of_unity=False)
	This method defines shape functions and derivatives. More...
def	StrainToVoigt (M)
	This method transform the strains matrix to Voigt notation. More...
def	MatrixToVoigt (M)
	This method transform a symmetric matrix to Voigt notation. More...
def	ConvertTensorToVoigtMatrix (C)
	This method converts a 4th order tensor given to a matrix in Voigt notation. More...
def	ConvertVoigtMatrixToTensor (C)
	This method converts a matrix given in Voigt notation in a 4th order tensor. More...
def	DoubleContraction (A, B)
	This method performs the double contraction A:B. More...
def	MatrixB (DN)
	This method defines the deformation matrix B. More...
def	grad_sym_voigtform (DN, x)
	This method defines a symmetric gradient. More...
def	DfjDxi (DN, f)
	This method defines a gradient. More...
def	DfiDxj (DN, f)
	This method defines a gradient This returns a matrix D such that D(i,j) = D(fi)/D(xj). More...
def	div (DN, x)
	This method defines the divergence. More...
def	SubstituteMatrixValue (where_to_substitute, what_to_substitute, substituted_value)
	This method substitutes values into a matrix. More...
def	SubstituteScalarValue (where_to_substitute, what_to_substitute, substituted_value)
	This method substitutes values into a scalar. More...
def	SubstituteMatrixValueByVoigtSymbols (where_to_substitute, what_to_substitute, substituted_value, is_strain)
	This method substitutes values into a matrix. More...
def	Compute_RHS (functional, testfunc, do_simplifications=False)
	This computes the RHS vector. More...
def	Compute_LHS (rhs, testfunc, dofs, do_simplifications=False)
	This computes the LHS matrix. More...
def	Compute_RHS_and_LHS (functional, testfunc, dofs, do_simplifications=False)
	This computes the LHS matrix and the RHS vector. More...
def	OutputScalar (scalar_expression, name, language, indentation_level=0, replace_indices=True, assignment_op="=")
	This function generates code to assign to a (pre-declared) scalar. More...
def	OutputVector (vector_expression, name, language, indentation_level=0, replace_indices=True, assignment_op="=")
	This function generates code to fill a (pre-declared) vector. More...
def	OutputMatrix (matrix_expression, name, language, indentation_level=0, replace_indices=True, assignment_op="=")
	This function generates code to fill a (pre-declared) matrix. More...
def	OutputSymbolicVariable (expression, language, replace_indices=True)
	This function generates code from an expression. More...
def	OutputSymbolicVariableDeclaration (expression, name, language, indentation_level=0, replace_indices=True)
	This function generates code to declare and assign an expression, such as: More...
def	OutputMatrix_CollectingFactors (A, name, language, indentation_level=0, max_index=None, optimizations='basic', replace_indices=True, assignment_op="=")
	This method collects the constants of the replacement for matrices. More...
def	OutputVector_CollectingFactors (A, name, language, indentation_level=0, max_index=None, optimizations='basic', replace_indices=True, assignment_op="=")
	This method collects the constants of the replacement for vectors. More...
def	OutputScalar_CollectingFactors (A, name, language, indentation_level=0, optimizations='basic', replace_indices=True, assignment_op="=")
	This method collects the constants of the replacement for vectors. More...

Function Documentation

Compute_LHS()

def sympy_fe_utilities.Compute_LHS	(		rhs,
			testfunc,
			dofs,
			do_simplifications = False
	)

This computes the LHS matrix.

Keyword arguments:

• rhs – The RHS vector
• testfunc – The test functions
• dofs – The dofs vectors
• do_simplifications – If apply simplifications

Compute_RHS()

def sympy_fe_utilities.Compute_RHS	(		functional,
			testfunc,
			do_simplifications = False
	)

This computes the RHS vector.

Keyword arguments:

• functional – The functional to derivate
• testfunc – The test functions
• do_simplifications – If apply simplifications

Compute_RHS_and_LHS()

def sympy_fe_utilities.Compute_RHS_and_LHS	(		functional,
			testfunc,
			dofs,
			do_simplifications = False
	)

This computes the LHS matrix and the RHS vector.

Keyword arguments:

• functional – The functional to derivate
• testfunc – The test functions
• dofs – The dofs vectors
• do_simplifications – If apply simplifications

ConvertTensorToVoigtMatrix()

def sympy_fe_utilities.ConvertTensorToVoigtMatrix

(

C

)

This method converts a 4th order tensor given to a matrix in Voigt notation.

Keyword arguments:

• C – The 4th order tensor to be converted to Voigt notation

ConvertVoigtMatrixToTensor()

def sympy_fe_utilities.ConvertVoigtMatrixToTensor

(

C

)

This method converts a matrix given in Voigt notation in a 4th order tensor.

Keyword arguments:

• C – The matrix in Voigt notation to be converted to 4th order tensor

DefineMatrix()

def sympy_fe_utilities.DefineMatrix	(		name,
			m,
			n
	)

This method defines a symbolic matrix.

Keyword arguments:

• name – Name of variables.
• m – Number of rows.
• n – Number of columns.

DefineShapeFunctions()

def sympy_fe_utilities.DefineShapeFunctions	(		nnodes,
			dim,
			impose_partion_of_unity = False
	)

This method defines shape functions and derivatives.

Note that partition of unity is imposed the name HAS TO BE --> N and DN

Keyword arguments:

• nnodes – Number of nodes
• dim – Dimension of the space
• impose_partion_of_unity – Impose the partition of unity

DefineSymmetricFourthOrderTensor()

def sympy_fe_utilities.DefineSymmetricFourthOrderTensor	(		name,
			m,
			n,
			o,
			p
	)

This method defines a symbolic symmetric 4th order tensor.

Keyword arguments:

• name – Name of variables.
• m – 1st dimension.
• n – 2nd dimension.
• o – 3rd dimension.
• p – 4th dimension.

DefineSymmetricMatrix()

def sympy_fe_utilities.DefineSymmetricMatrix	(		name,
			m,
			n
	)

This method defines a symbolic symmetric matrix.

Keyword arguments:

• name – Name of variables.
• m – Number of rows.
• n – Number of columns.

DefineVector()

def sympy_fe_utilities.DefineVector	(		name,
			m
	)

This method defines a symbolic vector.

Keyword arguments:

• name – Name of variables.
• m – Number of components.

DfiDxj()

def sympy_fe_utilities.DfiDxj	(		DN,
			f
	)

This method defines a gradient This returns a matrix D such that D(i,j) = D(fi)/D(xj).

This is the standard in structural mechanics, that is: D(f1)/D(x1) D(f1)/D(x2) D(f1)/D(x3) D(f2)/D(x1) D(f2)/D(x2) D(f2)/D(x3) D(f3)/D(x1) D(f3)/D(x2) D(f3)/D(x3)

Keyword arguments:

• DN – The shape function derivatives
• f – The variable to compute the gradient

DfjDxi()

def sympy_fe_utilities.DfjDxi	(		DN,
			f
	)

This method defines a gradient.

Returns a matrix D such that D(i,j) = D(fj)/D(xi)

This is the standard in fluid dynamics, that is: D(f1)/D(x1) D(f2)/D(x1) D(f3)/D(x1) D(f1)/D(x2) D(f2)/D(x2) D(f3)/D(x2) D(f1)/D(x3) D(f2)/D(x3) D(f3)/D(x3)

Keyword arguments:

• DN – The shape function derivatives
• f– The variable to compute the gradient

div()

def sympy_fe_utilities.div	(		DN,
			x
	)

This method defines the divergence.

Keyword arguments:

• DN – The shape function derivatives
• x – The variable to compute the gradient

DoubleContraction()

def sympy_fe_utilities.DoubleContraction	(		A,
			B
	)

This method performs the double contraction A:B.

Keyword arguments:

• A – Left tensor
• B – Right tensor

grad_sym_voigtform()

def sympy_fe_utilities.grad_sym_voigtform	(		DN,
			x
	)

This method defines a symmetric gradient.

Keyword arguments:

• DN – The shape function derivatives
• x – The variable to compute the gradient

MatrixB()

def sympy_fe_utilities.MatrixB

(

DN

)

This method defines the deformation matrix B.

Keyword arguments:

• DN – The shape function derivatives

MatrixToVoigt()

def sympy_fe_utilities.MatrixToVoigt

(

M

)

This method transform a symmetric matrix to Voigt notation.

Keyword arguments:

• M – The input matrix

OutputMatrix()

def sympy_fe_utilities.OutputMatrix	(		matrix_expression,
			name,
			language,
			indentation_level = 0,
			replace_indices = True,
			assignment_op = "="
	)

This function generates code to fill a (pre-declared) matrix.

Keyword arguments:

• matrix_expression – The matrix
• name – The name of the variables
• language – The language of output
• indentation_level – The number of tabulations considered
• replace_indices – Set to True to replace matrix_i_j with matrix[i,j] (And similarly for vectors)
• assignment_op – The assignment operation

OutputMatrix_CollectingFactors()

def sympy_fe_utilities.OutputMatrix_CollectingFactors	(		A,
			name,
			language,
			indentation_level = 0,
			max_index = None,
			optimizations = 'basic',
			replace_indices = True,
			assignment_op = "="
	)

This method collects the constants of the replacement for matrices.

Keyword arguments:

• A – The factors
• name – The name of the constant
• language – The language of replacement
• indentation_level – The depth of the indentation (4 spaces per level)
• max_index – DEPRECATED The max number of indexes
• optimizations – The level of optimizations
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)
• assignment_op – The assignment operation

OutputScalar()

def sympy_fe_utilities.OutputScalar	(		scalar_expression,
			name,
			language,
			indentation_level = 0,
			replace_indices = True,
			assignment_op = "="
	)

This function generates code to assign to a (pre-declared) scalar.

Keyword arguments:

• scalar_expression – A scalar
• name – The name of the variables
• language – The language of output
• indentation_level – The number of tabulations considered
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)
• assignment_op – The assignment operation

OutputScalar_CollectingFactors()

def sympy_fe_utilities.OutputScalar_CollectingFactors	(		A,
			name,
			language,
			indentation_level = 0,
			optimizations = 'basic',
			replace_indices = True,
			assignment_op = "="
	)

This method collects the constants of the replacement for vectors.

Keyword arguments:

• A – The factors
• name – The name of the constant
• language – The language of replacement
• indentation_level – The depth of the indentation (4 spaces per level)
• optimizations – The level of optimizations
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)
• assignment_op – The assignment operation

OutputSymbolicVariable()

def sympy_fe_utilities.OutputSymbolicVariable	(		expression,
			language,
			replace_indices = True
	)

This function generates code from an expression.

Keyword arguments:

• expression – The expression to generate code from
• language – The language of output
• indentation_level – The number of tabulations considered
• max_index – The maximum index
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)

OutputSymbolicVariableDeclaration()

def sympy_fe_utilities.OutputSymbolicVariableDeclaration	(		expression,
			name,
			language,
			indentation_level = 0,
			replace_indices = True
	)

This function generates code to declare and assign an expression, such as:

{C++}
       const double variable = expression;

Keyword arguments:

• expression – The variable to define symbolic
• language – The language of output
• name – The name of the variables
• indentation_level – The number of tabulations considered
• max_index – DEPRECATED The maximum index
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)

OutputVector()

def sympy_fe_utilities.OutputVector	(		vector_expression,
			name,
			language,
			indentation_level = 0,
			replace_indices = True,
			assignment_op = "="
	)

This function generates code to fill a (pre-declared) vector.

Keyword arguments:

• rhs – The RHS vector
• name – The name of the variables
• language – The language of output
• indentation_level – The number of tabulations considered
• replace_indices – Set to True to replace matrix_i_j with matrix[i,j] (And similarly for vectors)
• assignment_op – The assignment operation

OutputVector_CollectingFactors()

def sympy_fe_utilities.OutputVector_CollectingFactors	(		A,
			name,
			language,
			indentation_level = 0,
			max_index = None,
			optimizations = 'basic',
			replace_indices = True,
			assignment_op = "="
	)

This method collects the constants of the replacement for vectors.

Keyword arguments:

• A – The factors
• name – The name of the constant
• language – The language of replacement
• indentation_level – The depth of the indentation (4 spaces per level)
• max_index – DEPRECATED The max number of indexes
• optimizations – The level of optimizations
• replace_indices – Set to True to replace matrix[i,j] with matrix_i_j (And similarly for vectors)
• assignment_op – The assignment operation

StrainToVoigt()

def sympy_fe_utilities.StrainToVoigt

(

M

)

This method transform the strains matrix to Voigt notation.

Keyword arguments:

• M – The strain matrix

SubstituteMatrixValue()

def sympy_fe_utilities.SubstituteMatrixValue	(		where_to_substitute,
			what_to_substitute,
			substituted_value
	)

This method substitutes values into a matrix.

Keyword arguments:

• where_to_substitute – Coordinates where to substitute
• what_to_substitute – Components to substitute
• substituted_value – Variable to substitute

SubstituteMatrixValueByVoigtSymbols()

def sympy_fe_utilities.SubstituteMatrixValueByVoigtSymbols	(		where_to_substitute,
			what_to_substitute,
			substituted_value,
			is_strain
	)

This method substitutes values into a matrix.

Note that this is intended to be used to substitute matrix indices by their corresponding Voigt ones

Keyword arguments:

• where_to_substitute – Coordinates where to substitute
• what_to_substitute – Components to substitute
• substituted_value – Variable to substitute
• is_strain – Flag indicating if substituted_value is a strain

SubstituteScalarValue()

def sympy_fe_utilities.SubstituteScalarValue	(		where_to_substitute,
			what_to_substitute,
			substituted_value
	)

This method substitutes values into a scalar.

Keyword arguments:

• where_to_substitute – Coordinates where to substitute
• what_to_substitute – Components to substitute
• substituted_value – Variable to substitute