!======================================================================! ! ! ! Software Name : FrontISTR Ver. 3.6 ! ! ! ! Module Name : lib ! ! ! ! Contact address : IIS,The University of Tokyo, CISS ! ! ! ! "Structural Analysis for Large Scale Assembly" ! ! ! ! Record of revision: ! ! Date Programmer Description of change ! ! ========= ========== ===================== ! ! YUAN Xi Original ! ! Nov.,2012 YUAN Xi Ortho added ! ! ! !======================================================================! !> \brief This module provides functions for elastic material module m_ElasticLinear use mMaterial implicit none integer, parameter, private :: kreal = kind(0.0d0) contains !> Calculate isotropic elastic matrix SUBROUTINE calElasticMatrix( matl, sectType, D, temp ) TYPE( tMaterial ), INTENT(IN) :: matl !> material properties INTEGER, INTENT(IN) :: sectType !> plane strain/stress or 3D REAL(KIND=kreal), INTENT(OUT) :: D(:,:) !> elastic matrix REAL(KIND=kreal), OPTIONAL :: temp !> temprature REAL(KIND=kreal) :: EE, PP, COEF1, COEF2, ina(1), outa(2) logical :: ierr D(:,:)=0.d0 if( present(temp) ) then ina(1) = temp call fetch_TableData( MC_ISOELASTIC, matl%dict, outa, ierr, ina ) if( ierr ) then ee = matl%variables(M_YOUNGS) pp = matl%variables(M_POISSON) else EE = outa(1) PP = outa(2) endif else call fetch_TableData( MC_ISOELASTIC, matl%dict, outa, ierr ) if( ierr ) then ee = matl%variables(M_YOUNGS) pp = matl%variables(M_POISSON) else EE = outa(1) PP = outa(2) endif endif SELECT CASE (sectType) CASE (D3) D(1,1)=EE*(1.d0-PP)/(1.d0-2.d0*PP)/(1.d0+PP) D(1,2)=EE*PP/(1.d0-2.d0*PP)/(1.d0+PP) D(1,3)=D(1,2) D(2,1)=D(1,2) D(2,2)=D(1,1) D(2,3)=D(1,2) D(3,1)=D(1,3) D(3,2)=D(2,3) D(3,3)=D(1,1) D(4,4)=EE/(1.d0+PP)*0.5d0 D(5,5)=EE/(1.d0+PP)*0.5d0 D(6,6)=EE/(1.d0+PP)*0.5d0 CASE (PlaneStress) COEF1=EE/(1.d0-PP*PP) COEF2=0.5d0*(1.d0-PP) D(1,1)=COEF1 D(1,2)=COEF1*PP D(1,3)=0.d0 D(2,1)=D(1,2) D(2,2)=D(1,1) D(2,3)=0.d0 D(3,1)=0.d0 D(3,2)=0.d0 D(3,3)=COEF1*COEF2 CASE (Planestrain) COEF1=EE/((1.d0+PP)*(1.d0-2.d0*PP)) COEF2=EE/(2.d0*(1.d0+PP)) D(1,1)=COEF1*(1.d0-PP) D(1,2)=COEF1*PP D(1,3)=0.d0 D(2,1)=D(1,2) D(2,2)=D(1,1) D(2,3)=0.d0 D(3,1)=0.d0 D(3,2)=0.d0 D(3,3)=COEF2 CASE (AxisSymetric) COEF1=EE*(1.d0-PP)/((1.d0+PP)*(1.d0-2.d0*PP)) COEF2=(1.d0-2.d0*PP)/(2.d0*(1.d0-PP)) D(1,1)=COEF1 D(1,2)=COEF1*PP/(1.d0-PP) D(1,3)=0.d0 D(1,4)=D(1,2) D(2,1)=D(1,2) D(2,2)=D(1,1) D(2,3)=0.d0 D(2,4)=D(1,2) D(3,1)=0.d0 D(3,2)=0.d0 D(3,3)=COEF1*COEF2 D(3,4)=0.d0 D(4,1)=D(1,4) D(4,2)=D(2,4) D(4,3)=0.d0 D(4,4)=D(1,1) CASE DEFAULT STOP "Section type not defined" END SELECT END SUBROUTINE !> Calculate orthotropic elastic matrix SUBROUTINE calElasticMatrix_ortho( matl, sectType, bij, DMAT, temp ) use m_utilities TYPE( tMaterial ), INTENT(IN) :: matl !> material properties INTEGER, INTENT(IN) :: sectType !> plane strain/stress or 3D REAL(KIND=kreal), INTENT(IN) :: bij(3,3) !> director REAL(KIND=kreal), INTENT(OUT) :: DMAT(:,:) !> elastic matrix REAL(KIND=kreal), OPTIONAL :: temp !> temprature REAL(KIND=kreal) :: E1, E2, E3, G12, G23, G13, nyu12, nyu23,nyu13 REAL(KIND=kreal) :: nyu21,nyu32,nyu31, delta1, ina(1), outa(9) REAL(KIND=kreal) :: tm(6,6) logical :: ierr if( present(temp) ) then ina(1) = temp call fetch_TableData( MC_ORTHOELASTIC, matl%dict, outa, ierr, ina ) if( ierr ) then stop "Fails in fetching orthotropic elastic constants!" endif else call fetch_TableData( MC_ORTHOELASTIC, matl%dict, outa, ierr ) if( ierr ) then stop "Fails in fetching orthotropic elastic constants!" endif endif E1 = outa(1) E2 = outa(2) E3 = outa(3) nyu12 = outa(4) nyu13 = outa(5) nyu23 = outa(6) G12 = outa(7) G13 = outa(8) G23 = outa(9) nyu21 = E2/E1*nyu12 nyu32 = E3/E2*nyu23 nyu31 = E3/E1*nyu13 delta1 = 1.d0/(1.d0 -nyu12*nyu21 -nyu23*nyu32 -nyu31*nyu13 -2.d0*nyu21*nyu32*nyu13) DMAT(:,:)=0.d0 DMAT(1,1) = E1*(1.d0-nyu23*nyu32)*delta1 DMAT(2,2) = E2*(1.d0-nyu13*nyu31)*delta1 DMAT(3,3) = E3*(1.d0-nyu12*nyu21)*delta1 DMAT(1,2) = E1*(nyu21+nyu31*nyu23)*delta1 DMAT(1,3) = E1*(nyu31+nyu21*nyu32)*delta1 DMAT(2,3) = E2*(nyu32+nyu12*nyu31)*delta1 DMAT(4,4) = G12 DMAT(5,5) = G23 DMAT(6,6) = G13 DMAT(2,1) = DMAT(1,2) DMAT(3,2) = DMAT(2,3) DMAT(3,1) = DMAT(1,3) call transformation(bij, tm) dmat = matmul( transpose(tm), dmat) dmat = matmul( dmat, (tm) ) END SUBROUTINE !< calculate contravariant elastic tensor !#################################################################### SUBROUTINE LinearElastic_Shell & (matl, sectType, c, & e1_hat, e2_hat, e3_hat, cg1, cg2, cg3, & alpha, n_layer) !#################################################################### TYPE( tMaterial ), INTENT(IN) :: matl INTEGER, INTENT(IN) :: sectType, n_layer REAL(KIND = kreal), INTENT(OUT) :: c(:, :, :, :) REAL(KIND = kreal), INTENT(IN) :: e1_hat(3), e2_hat(3), e3_hat(3) !< local Orthonormal frame REAL(KIND = kreal), INTENT(IN) :: cg1(3), cg2(3), cg3(3) !< contravaraint frame REAL(KIND = kreal), INTENT(OUT) :: alpha !-------------------------------------------------------------------- REAL(KIND = kreal) :: ee, pp, ee2, g12, g23, g31, theta, pp2 REAL(KIND = kreal) :: coef1, coef2 REAL(KIND = kreal) :: outa(2) REAL(KIND = kreal) :: lambda1, lambda2, mu, k_correction REAL(KIND = kreal) :: c_hat(3, 3, 3, 3), D(5,5), D_hat(5,5), D_temp(5,5), T(5,5) REAL(KIND = kreal) :: e_hat_dot_cg(3, 3) REAL(KIND = kreal) :: alpha_over_mu INTEGER :: index_i(5), index_j(5), index_k(5), index_l(5) INTEGER :: is, js, ii, ij, ik, il INTEGER :: i, j, k, l, total_layer, matl_type LOGICAL :: ierr !-------------------------------------------------------------------- CALL fetch_TableData(MC_ISOELASTIC, matl%dict, outa, ierr) !-------------------------------------------------------------------- matl_type = int(matl%variables(M_SHELL_MATLTYPE)) IF(matl_type == 0)THEN IF( ierr ) THEN total_layer = int(matl%variables(M_TOTAL_LAYER)) IF( total_layer .ge. 2) THEN ee = matl%variables(100+3*n_layer-2) pp = matl%variables(100+3*n_layer-1) alpha_over_mu = matl%variables(M_ALPHA_OVER_MU) ELSE ee = matl%variables(M_YOUNGS) pp = matl%variables(M_POISSON) alpha_over_mu = matl%variables(M_ALPHA_OVER_MU) END IF ELSE ee = outa(1) pp = outa(2) alpha_over_mu = matl%variables(M_ALPHA_OVER_MU) END IF !-------------------------------------------------------------------- ! Elastic constant lambda1 = ee/( 1.0D0-pp*pp ) lambda2 = pp*lambda1 mu = 0.5D0*ee/( 1.0D0+pp ) !-------------------------------------------------------------------- ! Shear correction factor k_correction = 5.0D0/6.0D0 !k_correction = 1.0D0 !-------------------------------------------------------------------- alpha = alpha_over_mu*mu !-------------------------------------------------------------------- ! Constitutive tensor c_hat(:, :, :, :) = 0.0D0 !-------------------------------------------------------- c_hat(1, 1, 1, 1) = lambda1 c_hat(1, 1, 2, 2) = lambda2 c_hat(2, 2, 1, 1) = lambda2 c_hat(2, 2, 2, 2) = lambda1 c_hat(1, 2, 1, 2) = mu c_hat(1, 2, 2, 1) = mu c_hat(2, 1, 1, 2) = mu c_hat(2, 1, 2, 1) = mu c_hat(1, 3, 1, 3) = k_correction*mu c_hat(1, 3, 3, 1) = k_correction*mu c_hat(2, 3, 2, 3) = k_correction*mu c_hat(2, 3, 3, 2) = k_correction*mu c_hat(3, 1, 3, 1) = k_correction*mu c_hat(3, 1, 1, 3) = k_correction*mu c_hat(3, 2, 3, 2) = k_correction*mu c_hat(3, 2, 2, 3) = k_correction*mu !-------------------------------------------------------- ELSEIF(matl_type == 1)THEN ! write(*,*) 'TOTAL_LAYER', matl%variables(M_TOTAL_LAYER) total_layer = int(matl%variables(M_TOTAL_LAYER)) ee = matl%variables(100+8*n_layer-7) pp = matl%variables(100+8*n_layer-6) ee2 = matl%variables(100+8*n_layer-4) g12 = matl%variables(100+8*n_layer-3) g23 = matl%variables(100+8*n_layer-2) g31 = matl%variables(100+8*n_layer-1) theta = matl%variables(100+8*n_layer) alpha_over_mu = matl%variables(M_ALPHA_OVER_MU) !-------------------------------------------------------------------- ! Shear correction factor k_correction = 5.0D0/6.0D0 !-------------------------------------------------------------------- alpha = alpha_over_mu * 0.5D0 * ee / ( 1.0D0+pp ) !-------------------------------------------------------------------- ! write(*,*) ee,pp,ee2,g12,g23,g31,theta,alpha_over_mu,n_layer D(:,:) = 0.0D0 D_hat(:,:) = 0.0D0 D_temp(:,:) = 0.0D0 T(:,:) = 0.0D0 pp2 = pp * ee2 / ee D(1,1) = ee / (1.0D0 - pp * pp2) D(1,2) = pp2 * ee / (1.0D0- pp * pp2) D(2,1) = pp2 * ee / (1.0D0- pp * pp2) D(2,2) = ee2 / (1.0D0 - pp * pp2) D(3,3) = g12 D(4,4) = g23 D(5,5) = g31 T(1,1) = cos(theta) * cos(theta) T(1,2) = sin(theta) * sin(theta) T(2,1) = sin(theta) * sin(theta) T(2,2) = cos(theta) * cos(theta) T(3,3) = cos(theta) * cos(theta) - sin(theta) * sin(theta) T(1,3) = sin(theta) * cos(theta) T(2,3) = -sin(theta) * cos(theta) T(3,1) = -2.0D0 * sin(theta) * cos(theta) T(3,2) = 2.0D0 * sin(theta) * cos(theta) T(4,4) = cos(theta) T(4,5) = sin(theta) T(5,4) = -sin(theta) T(5,5) = cos(theta) !--------------------- D_temp = [D]*[T] D_temp(1,1) = D(1,1)*T(1,1)+D(1,2)*T(2,1) D_temp(1,2) = D(1,1)*T(1,2)+D(1,2)*T(2,2) D_temp(2,1) = D(2,1)*T(1,1)+D(2,2)*T(2,1) D_temp(2,2) = D(2,1)*T(1,2)+D(2,2)*T(2,2) D_temp(3,1) = D(3,3)*T(3,1) D_temp(3,2) = D(3,3)*T(3,2) D_temp(1,3) = D(1,1)*T(1,3)+D(1,2)*T(2,3) D_temp(2,3) = D(2,1)*T(1,3)+D(2,2)*T(2,3) D_temp(3,3) = D(3,3)*T(3,3) D_temp(4,4) = D(4,4)*T(4,4) D_temp(4,5) = D(4,4)*T(4,5) D_temp(5,4) = D(5,5)*T(5,4) D_temp(5,5) = D(5,5)*T(5,5) !--------------------- D_hat = [trans_T]*[D_temp] D_hat(1,1) = T(1,1)*D_temp(1,1)+T(1,2)*D_temp(2,1)+T(3,1)*D_temp(3,1) D_hat(1,2) = T(1,1)*D_temp(1,2)+T(1,2)*D_temp(2,2)+T(3,1)*D_temp(3,2) D_hat(2,1) = T(2,1)*D_temp(1,1)+T(2,2)*D_temp(2,1)+T(3,2)*D_temp(3,1) D_hat(2,2) = T(2,1)*D_temp(1,2)+T(2,2)*D_temp(2,2)+T(3,2)*D_temp(3,2) D_hat(3,1) = T(1,3)*D_temp(1,1)+T(2,3)*D_temp(2,1)+T(3,3)*D_temp(3,1) D_hat(3,2) = T(1,3)*D_temp(1,2)+T(2,3)*D_temp(2,2)+T(3,3)*D_temp(3,2) D_hat(1,3) = T(1,1)*D_temp(1,3)+T(1,2)*D_temp(2,3)+T(3,1)*D_temp(3,3) D_hat(2,3) = T(2,1)*D_temp(1,3)+T(2,2)*D_temp(2,3)+T(3,2)*D_temp(3,3) D_hat(3,3) = T(1,3)*D_temp(1,3)+T(2,3)*D_temp(2,3)+T(3,3)*D_temp(3,3) D_hat(4,4) = T(4,4)*D_temp(4,4)+T(5,4)*D_temp(5,4) D_hat(4,5) = T(4,4)*D_temp(4,5)+T(5,4)*D_temp(5,5) D_hat(5,4) = T(4,5)*D_temp(4,4)+T(5,5)*D_temp(5,4) D_hat(5,5) = T(4,5)*D_temp(4,5)+T(5,5)*D_temp(5,5) !-------------------------------------------------------------------- ! Constitutive tensor c_hat(:, :, :, :) = 0.0D0 !write(*,*) 'Elastic linear.f90 make c_hat' !-------D_hat to c_hat index_i(1) = 1 index_i(2) = 2 index_i(3) = 1 index_i(4) = 2 index_i(5) = 3 index_j(1) = 1 index_j(2) = 2 index_j(3) = 2 index_j(4) = 3 index_j(5) = 1 index_k(1) = 1 index_k(2) = 2 index_k(3) = 1 index_k(4) = 2 index_k(5) = 3 index_l(1) = 1 index_l(2) = 2 index_l(3) = 2 index_l(4) = 3 index_l(5) = 1 !-------------------------------------------------------------------- DO js = 1, 5 DO is = 1, 5 ii = index_i(is) ij = index_j(is) ik = index_k(js) il = index_l(js) c_hat(ii, ij, ik, il) = D_hat(is, js) END DO END DO !-------------------------------------------------------- ELSE write(*,*) 'shell matl type isnot collect' stop ENDIF SELECT CASE( sectType ) CASE( Shell ) e_hat_dot_cg(1, 1) & = e1_hat(1)*cg1(1)+e1_hat(2)*cg1(2) & +e1_hat(3)*cg1(3) e_hat_dot_cg(2, 1) & = e2_hat(1)*cg1(1)+e2_hat(2)*cg1(2) & +e2_hat(3)*cg1(3) e_hat_dot_cg(3, 1) = 0.0D0 e_hat_dot_cg(1, 2) & = e1_hat(1)*cg2(1)+e1_hat(2)*cg2(2) & +e1_hat(3)*cg2(3) e_hat_dot_cg(2, 2) & = e2_hat(1)*cg2(1)+e2_hat(2)*cg2(2) & +e2_hat(3)*cg2(3) e_hat_dot_cg(3, 2) = 0.0D0 e_hat_dot_cg(1, 3) & = e1_hat(1)*cg3(1)+e1_hat(2)*cg3(2) & +e1_hat(3)*cg3(3) e_hat_dot_cg(2, 3) & = e2_hat(1)*cg3(1)+e2_hat(2)*cg3(2) & +e2_hat(3)*cg3(3) e_hat_dot_cg(3, 3) & = e3_hat(1)*cg3(1)+e3_hat(2)*cg3(2) & +e3_hat(3)*cg3(3) !-------------------------------------------------------- ! Constitutive tensor c(1, 1, 1, 1) = 0.0D0 c(2, 2, 1, 1) = 0.0D0 c(1, 2, 1, 1) = 0.0D0 c(2, 2, 2, 2) = 0.0D0 c(1, 2, 2, 2) = 0.0D0 c(1, 2, 1, 2) = 0.0D0 c(3, 1, 1, 1) = 0.0D0 c(3, 1, 2, 2) = 0.0D0 c(3, 1, 1, 2) = 0.0D0 c(2, 3, 1, 1) = 0.0D0 c(2, 3, 2, 2) = 0.0D0 c(2, 3, 1, 2) = 0.0D0 c(3, 1, 3, 1) = 0.0D0 c(3, 1, 2, 3) = 0.0D0 c(2, 3, 2, 3) = 0.0D0 DO l = 1, 2 DO k = 1, 2 DO j = 1, 2 DO i = 1, 2 c(1, 1, 1, 1) & = c(1, 1, 1, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 1)*e_hat_dot_cg(j ,1) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 1) c(2, 2, 1, 1) & = c(2, 2, 1, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 2) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 1) c(1, 2, 1, 1) & = c(1, 2, 1, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 1)*e_hat_dot_cg(j, 2) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 1) c(2, 2, 2, 2) & = c(2, 2, 2, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 2) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 2) c(1, 2, 2, 2) & = c(1, 2, 2, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 1)*e_hat_dot_cg(j, 2) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 2) c(1, 2, 1, 2) & = c(1, 2, 1, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 1)*e_hat_dot_cg(j, 2) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 2) END DO DO i = 1, 3 c(3, 1, 1, 1) & = c(3, 1, 1, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 3)*e_hat_dot_cg(j, 1) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 1) c(3, 1, 2, 2) & = c(3, 1, 2, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 3)*e_hat_dot_cg(j, 1) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 2) c(3, 1, 1, 2) & = c(3, 1, 1, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 3)*e_hat_dot_cg(j, 1) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 2) END DO END DO DO j = 1, 3 DO i = 1, 2 c(2, 3, 1, 1) & = c(2, 3, 1, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 3) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 1) c(2, 3, 2, 2) & = c(2, 3, 2, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 3) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 2) c(2, 3, 1, 2) & = c(2, 3, 1, 2) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 3) & *e_hat_dot_cg(k, 1)*e_hat_dot_cg(l, 2) END DO END DO END DO DO k = 1, 3 DO j = 1, 2 DO i = 1, 3 c(3, 1, 3, 1) & = c(3, 1, 3, 1) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 3)*e_hat_dot_cg(j, 1) & *e_hat_dot_cg(k, 3)*e_hat_dot_cg(l, 1) END DO END DO END DO END DO DO l = 1, 3 DO k = 1, 2 DO j = 1, 2 DO i = 1, 3 c(3, 1, 2, 3) & = c(3, 1, 2, 3) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 3)*e_hat_dot_cg(j, 1) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 3) END DO END DO DO j = 1, 3 DO i = 1, 2 c(2, 3, 2, 3) & = c(2, 3, 2, 3) & +c_hat(i, j, k, l) & *e_hat_dot_cg(i, 2)*e_hat_dot_cg(j, 3) & *e_hat_dot_cg(k, 2)*e_hat_dot_cg(l, 3) END DO END DO END DO END DO c(1, 1, 2, 2) = c(2, 2, 1, 1) c(1, 1, 1, 2) = c(1, 2, 1, 1) c(1, 1, 2, 3) = c(2, 3, 1, 1) c(1, 1, 3, 1) = c(3, 1, 1, 1) c(2, 2, 1, 2) = c(1, 2, 2, 2) c(2, 2, 2, 3) = c(2, 3, 2, 2) c(2, 2, 3, 1) = c(3, 1, 2, 2) c(1, 2, 2, 3) = c(2, 3, 1, 2) c(1, 2, 3, 1) = c(3, 1, 1, 2) c(2, 3, 3, 1) = c(3, 1, 2, 3) !-------------------------------------------------------- ! DO l = 1, 3 ! ! DO k = 1, 3 ! ! DO j = 1, 3 ! ! DO i = 1, 3 ! ! c(i, j, k, l) = 0.0D0 ! ! DO ll = 1, 3 ! ! DO kk = 1, 3 ! ! DO jj = 1, 3 ! ! DO ii = 1, 3 ! ! c(i, j, k, l) & ! = c(i, j, k, l) & ! +c_hat(ii, jj, kk, ll) & ! *e_hat_dot_cg(ii, i)*e_hat_dot_cg(jj, j) & ! *e_hat_dot_cg(kk, k)*e_hat_dot_cg(ll, l) ! ! END DO ! ! END DO ! ! END DO ! ! END DO ! ! END DO ! ! END DO ! ! END DO ! ! END DO !-------------------------------------------------------- END SELECT !-------------------------------------------------------------------- RETURN !#################################################################### END SUBROUTINE LinearElastic_Shell !#################################################################### ! > (Gaku Hashimoto, The University of Tokyo, 2012/11/15) end module m_ElasticLinear