Kratos::DiscontinuousShapeFunctionsUtilities Class Reference

#include <discont_utils.h>

Collaboration diagram for Kratos::DiscontinuousShapeFunctionsUtilities:

Static Public Member Functions
static int	CalculateDiscontinuousShapeFunctions (BoundedMatrix< double,(3+1), 3 > &rPoints, BoundedMatrix< double,(3+1), 3 > &DN_DX, array_1d< double,(3+1)> &rDistances, array_1d< double,(3 *(3-1))> &rVolumes, BoundedMatrix< double, 3 *(3-1),(3+1) > &rShapeFunctionValues, array_1d< double,(3 *(3-1))> &rPartitionsSign, std::vector< Matrix > &rGradientsValue, BoundedMatrix< double, 3 *(3-1),(3+1)> &Nenriched, array_1d< double, 6 > &edge_areas)
static int	CalculateDiscontinuousShapeFunctions (const BoundedMatrix< double,(2+1), 2 > &rPoints, BoundedMatrix< double,(2+1), 2 > &rDN_DX, array_1d< double,(2+1)> &rDistances, array_1d< double,(3 *(2-1))> &rVolumes, BoundedMatrix< double, 3 *(2-1),(2+1) > &rGPShapeFunctionValues, array_1d< double,(3 *(2-1))> &rPartitionsSign, std::vector< Matrix > &rGradientsValue, BoundedMatrix< double, 3 *(2-1),(2+1)> &rNenriched, array_1d< double, 3 > &rEdgeAreas)
static int	CalculateDiscontinuousShapeFunctionsInLocalAxis (BoundedMatrix< double,(2+1), 2 > &rOriginalPoints, BoundedMatrix< double,(2+1), 2 > &rRotatedPoints, BoundedMatrix< double,(2+1), 2 > &DN_DX_original, array_1d< double,(2+1)> &rDistances, array_1d< double,(3 *(2-1))> &rVolumes, BoundedMatrix< double, 3 *(2-1),(2+1) > &rGPShapeFunctionValues, array_1d< double,(3 *(2-1))> &rPartitionsSign, std::vector< Matrix > &rGradientsValue, BoundedMatrix< double, 3 *(2-1),(2+1)> &Nenriched, BoundedMatrix< double,(2), 2 > &rRotationMatrix, BoundedMatrix< double,(2+1), 2 > &DN_DX_in_local_axis)

Detailed Description

This utility can be used to calculate the discontinuous shape function for tetrahedra element. The metodology consists in partitioning the tetrahedra in a set of sub-tetrahedra and cacluate the new shape functions using these partitions.

Member Function Documentation

CalculateDiscontinuousShapeFunctions() [1/2]

static int Kratos::DiscontinuousShapeFunctionsUtilities::CalculateDiscontinuousShapeFunctions ( BoundedMatrix< double,(3+1), 3 > &  rPoints, BoundedMatrix< double,(3+1), 3 > &  DN_DX, array_1d< double,(3+1)> &  rDistances, array_1d< double,(3 *(3-1))> &  rVolumes, BoundedMatrix< double, 3 *(3-1),(3+1) > &  rShapeFunctionValues, array_1d< double,(3 *(3-1))> &  rPartitionsSign, std::vector< Matrix > &  rGradientsValue, BoundedMatrix< double, 3 *(3-1),(3+1)> &  Nenriched, array_1d< double, 6 > &  edge_areas  )

inlinestatic

The method to calculate the discontinuous shape functions for given tetrahedra.

Parameters

rPoints	A 4x3 matrix where row i has the coordinates of node i.
DN_DX	The gradient of the shape functions Ni respect to the reference coordinates
rDistances	is an input vector of 4 size which holds relative distance (not need to be exact) for each node. it is used internally to mark the position of the zero level
rVolumes	Result vector with size 6 (maximumn number of partitions) holding the volume of each partition
rShapeFunctionValues	Result 6x4 matrix where each row represents a partition and holds the shape functions N1 to N4 of the original tetrahedra evaluated in the gauss point (center) of the partition. so that it is N(gauss_index, node_index)
rPartitionsSign	A result vector of 6 holding the sign of the distance for the partition. The value -1 represents the negative distance sign, 1 represents positive distance and 0 stands for not used partition
rGradientsValue	Restult vector of size 6 holding the gradient of the enriched shape funciton for each volume. Each element of vector is a 1x3 matrix representing the gradient of enriched shape function. The use of matrix is for possible future improvement.
Nenriched	is a Matrix that contains for every gauss point the values of the enriched shape functions at the position of the gauss point so that Nenriched(1,0) contains the value of the enriched shape function "0" at the gauss point "1"

Returns

number of partitions created which can be from 1 to 6. 1 holds for only 1 partition which is the original element. (No partitioning needed)

CalculateDiscontinuousShapeFunctions() [2/2]

static int Kratos::DiscontinuousShapeFunctionsUtilities::CalculateDiscontinuousShapeFunctions ( const BoundedMatrix< double,(2+1), 2 > &  rPoints, BoundedMatrix< double,(2+1), 2 > &  rDN_DX, array_1d< double,(2+1)> &  rDistances, array_1d< double,(3 *(2-1))> &  rVolumes, BoundedMatrix< double, 3 *(2-1),(2+1) > &  rGPShapeFunctionValues, array_1d< double,(3 *(2-1))> &  rPartitionsSign, std::vector< Matrix > &  rGradientsValue, BoundedMatrix< double, 3 *(2-1),(2+1)> &  rNenriched, array_1d< double, 3 > &  rEdgeAreas  )

inlinestatic

CalculateDiscontinuousShapeFunctionsInLocalAxis()

static int Kratos::DiscontinuousShapeFunctionsUtilities::CalculateDiscontinuousShapeFunctionsInLocalAxis ( BoundedMatrix< double,(2+1), 2 > &  rOriginalPoints, BoundedMatrix< double,(2+1), 2 > &  rRotatedPoints, BoundedMatrix< double,(2+1), 2 > &  DN_DX_original, array_1d< double,(2+1)> &  rDistances, array_1d< double,(3 *(2-1))> &  rVolumes, BoundedMatrix< double, 3 *(2-1),(2+1) > &  rGPShapeFunctionValues, array_1d< double,(3 *(2-1))> &  rPartitionsSign, std::vector< Matrix > &  rGradientsValue, BoundedMatrix< double, 3 *(2-1),(2+1)> &  Nenriched, BoundedMatrix< double,(2), 2 > &  rRotationMatrix, BoundedMatrix< double,(2+1), 2 > &  DN_DX_in_local_axis  )

inlinestatic

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The documentation for this class was generated from the following file:

• /home/runner/work/Documentation/Documentation/master/kratos/utilities/discont_utils.h