ProcessLib::NonLinearBMatrix Namespace Reference

Functions
template<int DisplacementDim, int NPOINTS, typename BMatrixType , typename GradientVectorType , typename N_Type , typename DNDX_Type >
BMatrixType	computeBMatrix (DNDX_Type const &dNdx, N_Type const &N, GradientVectorType const &grad_u, const double radius, const bool is_axially_symmetric)

Function Documentation

computeBMatrix()

template<int DisplacementDim, int NPOINTS, typename BMatrixType , typename GradientVectorType , typename N_Type , typename DNDX_Type >

BMatrixType ProcessLib::NonLinearBMatrix::computeBMatrix	(	DNDX_Type const &	dNdx,
		N_Type const &	N,
		GradientVectorType const &	grad_u,
		const double	radius,
		const bool	is_axially_symmetric )

Fills a non linear B-matrix based on given shape function dN/dx values and displacement gradient.

Definition at line 29 of file NonLinearBMatrix.h.

{
    static_assert(0 < DisplacementDim && DisplacementDim <= 3,
                  "NonLinearBMatrix::computeBMatrix: DisplacementDim must be "
                  "in range [1,3].");
 
    BMatrixType B = BMatrixType::Zero(
        MathLib::KelvinVector::kelvin_vector_dimensions(DisplacementDim),
        NPOINTS * DisplacementDim);
 
    switch (DisplacementDim)
    {
        case 3:
            for (int i = 0; i < NPOINTS; ++i)
            {
                B(0, i) = dNdx(0, i) * grad_u[0];
                B(1, i) = dNdx(1, i) * grad_u[1];
                B(2, i) = dNdx(2, i) * grad_u[2];
 
                B(0, NPOINTS + i) = dNdx(0, i) * grad_u[3];
                B(1, NPOINTS + i) = dNdx(1, i) * grad_u[4];
                B(2, NPOINTS + i) = dNdx(2, i) * grad_u[5];
 
                B(0, 2 * NPOINTS + i) = dNdx(0, i) * grad_u[6];
                B(1, 2 * NPOINTS + i) = dNdx(1, i) * grad_u[7];
                B(2, 2 * NPOINTS + i) = dNdx(2, i) * grad_u[8];
 
                B(3, i) = (dNdx(1, i) * grad_u[0] + dNdx(0, i) * grad_u[1]) /
                          std::sqrt(2);
                B(4, i) = (dNdx(2, i) * grad_u[1] + dNdx(1, i) * grad_u[2]) /
                          std::sqrt(2);
                B(5, i) = (dNdx(2, i) * grad_u[0] + dNdx(0, i) * grad_u[2]) /
                          std::sqrt(2);
 
                B(3, NPOINTS + i) =
                    (dNdx(1, i) * grad_u[3] + dNdx(0, i) * grad_u[4]) /
                    std::sqrt(2);
                B(4, NPOINTS + i) =
                    (dNdx(2, i) * grad_u[4] + dNdx(1, i) * grad_u[5]) /
                    std::sqrt(2);
                B(5, NPOINTS + i) =
                    (dNdx(2, i) * grad_u[3] + dNdx(0, i) * grad_u[5]) /
                    std::sqrt(2);
 
                B(3, 2 * NPOINTS + i) =
                    (dNdx(1, i) * grad_u[6] + dNdx(0, i) * grad_u[7]) /
                    std::sqrt(2);
                B(4, 2 * NPOINTS + i) =
                    (dNdx(2, i) * grad_u[7] + dNdx(1, i) * grad_u[8]) /
                    std::sqrt(2);
                B(5, 2 * NPOINTS + i) =
                    (dNdx(2, i) * grad_u[6] + dNdx(0, i) * grad_u[8]) /
                    std::sqrt(2);
            }
            break;
        case 2:
            for (int i = 0; i < NPOINTS; ++i)
            {
                B(0, i) = dNdx(0, i) * grad_u[0];
                B(1, i) = dNdx(1, i) * grad_u[1];
                // B(2, i) = 0;
 
                B(0, NPOINTS + i) = dNdx(0, i) * grad_u[2];
                B(1, NPOINTS + i) = dNdx(1, i) * grad_u[3];
                // B(2, NPOINTS + i) = 0;
 
                B(3, i) = (dNdx(1, i) * grad_u[0] + dNdx(0, i) * grad_u[1]) /
                          std::sqrt(2);
                B(3, NPOINTS + i) =
                    (dNdx(1, i) * grad_u[2] + dNdx(0, i) * grad_u[3]) /
                    std::sqrt(2);
            }
            if (is_axially_symmetric)
            {
                for (int i = 0; i < NPOINTS; ++i)
                {
                    B(2, i) = grad_u[4] * N[i] / radius;
                }
            }
            break;
        default:
            break;
    }
 
    return B;
}

References MathLib::KelvinVector::kelvin_vector_dimensions().

Referenced by ProcessLib::LargeDeformation::LargeDeformationLocalAssembler< ShapeFunction, DisplacementDim >::assembleWithJacobian(), and ProcessLib::LargeDeformation::LargeDeformationLocalAssembler< ShapeFunction, DisplacementDim >::updateConstitutiveRelations().