��sr!com.femlab.server.ModelFileHeader�D���%LtagstLcom/femlab/util/FlStringList;Ltypesq~LvrsntLcom/femlab/util/FlVersion;xpwsrcom.femlab.util.FlVersion��%�/B =IbuildImajorLdatetLjava/lang/String;Lextq~Lnameq~Lrcsq~L reactionExtq~L reactionNameq~xpwtq~t#COMSOL Reaction Engineering Lab 3.5tat COMSOL 3.5q~ w`t$Name: v35ap $t$Date: 2009/05/11 07:38:49 $xur[Ljava.lang.String;��V��{Gxp t modelinfotxfemtguitfem0tg2tg3tfem5q~q~tfem10tfem10.0q~q~uq~ q~t femstructt guistructq~tdrawq~tgeomtsolutiontxmeshq~tmeshq~q~xsrcom.femlab.api.client.ModelInfo�^���%Ldescrq~LdocURLq~[imaget[Bxpwur[B���T�xp !�PNG  IHDR��p����IDATx��Y�\G��ݺ�t���^��x!��!$8Q����ȏ��x�? E�_@� (�� ��"D�ؑd�;�س{�^oq���v;ɓ݈v��T*UU߶�۟�9Uwz&r� �8s )��))��)��))��))�))��))�))��))��)��))��)��))��))�))��))�))��))��)��))��)��))��))�))��))�))��))��)��))��܂�;�V�����z���������ݝ����s)�s���acc�ҥ�D�+���s�h�}:vC��lM�ٷ�*VVVΜ9����|]$r.~��JM���d"��[��8��H����J��'dS��2� �b\��� �EW���ȼHC�D���^������ܐ�產����5Kӵ�O0�$Od�&�D�<�,׮�с'�e�pP&��z�baj-��UN�D���dR���a����7e���F�-�� ��A�4�5*|�Nc���H}��Q�#@���_|��R� ��b��~t��7<���T3�io�R�oڮf�� ��0*���^T�v����7c �b.���� ��.�5{���SH ��zC={����0�>z.�۩�\y�^��X7_O���%��� )aDM��%d�Aʎ���/��+6��Qf��I�*���,ǟ��|��G�H ��̩��LZf�Z5+�s��)8o��Ľ�x����gd�*� 0)dž�or�i:z���o������!�F�(u�Ƀ��t�s\��! �ɞ�n�)at��c���ش0iGB�� uQ��݌��STǪ��:�^uT)u�e�d���BewC A1lbT�P2��Z8j �S_RC�ԗt��_��#��#%�����KU��9�C�1R�ؚ�U>]сNe5訚.��*E'�;��O��@ʱ`�i����P3��7(+�T�J��:֦:��yъ{���7�� R�Ș������H�-D�,UP��Z/j�������oE��=�qU�Ӝ�kR)a4�X�4��ZԦ�Q� �Rz�\��:qQ��� �q:"=�]� #�rl6:�^9}�G.���9�5���$�b��n��[�c��ӝ|�譺{W�ؕ�d��ߓ��ҨJ>%۟����tYu:���O9'7o�oߪ�q,����������Z��u}cx��a�/\��Y��J����ËY��ʾs�}��w����Y�Ξ�/�ѯ~���e�/n�2}FߒlFv�.w�,�˲x�?"���l_� *�8�/�ηۋ��\�.�^�Q�g���@�TᾸ���M�`i )�B<��Z�央��~�}a�����>�Z��Y|�~#AׯL���c��heY;.K�y�� #c��.vr�s�El[���� [T��m[Ӳ���� �nK�)a4D����k�g�u�B��kv�Y�5u�n�0�7;'�H�n }5Ǚ��`�_q6ݳ��2v�[�ܴ �-�)aT�[_�v-ӱ]�"h���v���f�g����*lZ%R���~eK���XM�)�t���-����w���7�ӭV�)aTl�����k�uʲ2,�r�ڗ�����<�y]'�H�n �&@)+ˎ��\{�t��O�[������wŊ�L��@��`���o"��JۦEYD����C����ЖU�!tNҟ�@����et,�"e�����C����a�ٷ�j����!%��?����/}ѽ���+�d����������݌�9�O5k7n,�;7I�#���Sτ����H H ����H H ��H H ����H H ��H H ����H H ����H ����H H ����H H�-�@Jx��/y¦�҈lIEND�B`�tpxuq~ t�` COMSOL 3.5 a 0 608 $Name: v35ap $ $Date: 2009/05/11 07:38:49 $ 2 geom on on off on off off on 0.1 t PiezoAxialSym axi {"uor","w","V"} {"r","phi","z"} smpaxi SME {"shlag(2,'uor')","shlag(2,'w')","shlag(2,'V')"} 4 2 2 on _smpaxi ephii_smpaxi eri_smpaxi erzi_smpaxi ezi_smpaxi sphii_smpaxi sri_smpaxi srzi_smpaxi szi_smpaxi Lag2 static freq symmetric_es off ref defined_by_structural_frame defined_by_structural_frame off {"lm1","lm2","lm3"} ideal 0 0 global global 0
0 0 0 0 0 0 {1,1,1,1,1,1}
0 0 global global 0
0 0 0 free axisym fixed fixed axisym free 0 0 0 0 0 0 0 0 nD0 ax V0 nD0 nD0 V 0 {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} 0 0 100 0 0 UP {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} 0 0 0 0 {5,4,2,6,3,1,1}
123 123 111 111 111 111 {"0","0","0"} {"0","0","0"} 1 iso piezoelectric global stress 1 0 2.5465E11 2.0e11 0 0.33 7500 mat1_rho {"0","0","0"} {"0","0","0"} {"16.5e-12","-4.78e-12","-8.45e-12","0","0","0","-4.78e-12","16.5e-12","-8.45e-12","0","0","0","-8.45e-12","-8.45e-12","20.7e-12","0","0","0","0","0","0","43.5e-12","0","0","0","0","0","0","43.5e-12","0","0","0","0","0","0","42.6e-12"} {"mat1_sE_1_1_","mat1_sE_2_1_","mat1_sE_3_1_","mat1_sE_4_1_","mat1_sE_5_1_","mat1_sE_6_1_","mat1_sE_1_2_","mat1_sE_2_2_","mat1_sE_3_2_","mat1_sE_4_2_","mat1_sE_5_2_","mat1_sE_6_2_","mat1_sE_1_3_","mat1_sE_2_3_","mat1_sE_3_3_","mat1_sE_4_3_","mat1_sE_5_3_","mat1_sE_6_3_","mat1_sE_1_4_","mat1_sE_2_4_","mat1_sE_3_4_","mat1_sE_4_4_","mat1_sE_5_4_","mat1_sE_6_4_","mat1_sE_1_5_","mat1_sE_2_5_","mat1_sE_3_5_","mat1_sE_4_5_","mat1_sE_5_5_","mat1_sE_6_5_","mat1_sE_1_6_","mat1_sE_2_6_","mat1_sE_3_6_","mat1_sE_4_6_","mat1_sE_5_6_","mat1_sE_6_6_"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"mat1_cE_1_1_","mat1_cE_2_1_","mat1_cE_3_1_","mat1_cE_4_1_","mat1_cE_5_1_","mat1_cE_6_1_","mat1_cE_1_2_","mat1_cE_2_2_","mat1_cE_3_2_","mat1_cE_4_2_","mat1_cE_5_2_","mat1_cE_6_2_","mat1_cE_1_3_","mat1_cE_2_3_","mat1_cE_3_3_","mat1_cE_4_3_","mat1_cE_5_3_","mat1_cE_6_3_","mat1_cE_1_4_","mat1_cE_2_4_","mat1_cE_3_4_","mat1_cE_4_4_","mat1_cE_5_4_","mat1_cE_6_4_","mat1_cE_1_5_","mat1_cE_2_5_","mat1_cE_3_5_","mat1_cE_4_5_","mat1_cE_5_5_","mat1_cE_6_5_","mat1_cE_1_6_","mat1_cE_2_6_","mat1_cE_3_6_","mat1_cE_4_6_","mat1_cE_5_6_","mat1_cE_6_6_"} {"0","0","-274e-12","0","0","-274e-12","0","0","593e-12","0","741e-12","0","741e-12","0","0","0","0","0"} {"mat1_d_1_1_","mat1_d_2_1_","mat1_d_3_1_","mat1_d_1_2_","mat1_d_2_2_","mat1_d_3_2_","mat1_d_1_3_","mat1_d_2_3_","mat1_d_3_3_","mat1_d_1_4_","mat1_d_2_4_","mat1_d_3_4_","mat1_d_1_5_","mat1_d_2_5_","mat1_d_3_5_","mat1_d_1_6_","mat1_d_2_6_","mat1_d_3_6_"} {"0","0","-6.62281","0","0","-6.62281","0","0","23.2403","0","17.0345","0","17.0345","0","0","0","0","0"} {"mat1_e_1_1_","mat1_e_2_1_","mat1_e_3_1_","mat1_e_1_2_","mat1_e_2_2_","mat1_e_3_2_","mat1_e_1_3_","mat1_e_2_3_","mat1_e_3_3_","mat1_e_1_4_","mat1_e_2_4_","mat1_e_3_4_","mat1_e_1_5_","mat1_e_2_5_","mat1_e_3_5_","mat1_e_1_6_","mat1_e_2_6_","mat1_e_3_6_"} {"3130","0","0","0","3130","0","0","0","3400"} {"mat1_epsilonrT_1_1_","mat1_epsilonrT_2_1_","mat1_epsilonrT_3_1_","mat1_epsilonrT_1_2_","mat1_epsilonrT_2_2_","mat1_epsilonrT_3_2_","mat1_epsilonrT_1_3_","mat1_epsilonrT_2_3_","mat1_epsilonrT_3_3_"} {"1704.40","0","0","0","1704.40","0","0","0","1433.61"} {"mat1_epsilonrS_1_1_","mat1_epsilonrS_2_1_","mat1_epsilonrS_3_1_","mat1_epsilonrS_1_2_","mat1_epsilonrS_2_2_","mat1_epsilonrS_3_2_","mat1_epsilonrS_1_3_","mat1_epsilonrS_2_3_","mat1_epsilonrS_3_3_"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"1","0","0","0","1","0","0","0","1"} {"1","0","0","0","1","0","0","0","1"} {"5.99e7","0","0","0","5.99e7","0","0","0","5.99e7"} {"5.99e7","0","0","0","5.99e7","0","0","0","5.99e7"} 1 5.99e7 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 xz nodamping 0 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} noloss noloss 0 0 global global 0
0 0 0 free 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 {"0","0"} {"0","0"} {1,2}
Wes_tot_smpaxi 8.854187817e-12
{"r","z"} {"ref"} {"shlag(2,'uor')","shlag(2,'w')","shlag(2,'V')"} 4 2 2 on 1
weak
SI {"0","0","0"} 111 {1,1} 12 123 111 111 111 111 {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"-(test(er_smpaxi)*sr_smpaxi+test(ephi_smpaxi)*sphi_smpaxi+test(ez_smpaxi)*sz_smpaxi+2*test(erz_smpaxi)*srz_smpaxi)*r","0","0"} {"-(test(er_smpaxi)*sr_smpaxi+test(ephi_smpaxi)*sphi_smpaxi+test(ez_smpaxi)*sz_smpaxi+2*test(erz_smpaxi)*srz_smpaxi)*r","0","r*(Dr_smpaxi*test(Er_smpaxi)+Dz_smpaxi*test(Ez_smpaxi))"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} 1 111 111 {"uor","w","V"} mat1_e_1_1_ mat1_e_1_2_ mat1_e_1_3_ mat1_e_1_4_ mat1_e_1_5_ mat1_e_1_6_ mat1_e_2_1_ mat1_e_2_2_ mat1_e_2_3_ mat1_e_2_4_ mat1_e_2_5_ mat1_e_2_6_ mat1_e_3_1_ mat1_e_3_2_ mat1_e_3_3_ mat1_e_3_4_ mat1_e_3_5_ mat1_e_3_6_ epsilon0_smpaxi*mat1_epsilonrS_1_1_ epsilon0_smpaxi*mat1_epsilonrS_1_2_ epsilon0_smpaxi*mat1_epsilonrS_1_3_ epsilon0_smpaxi*mat1_epsilonrS_2_2_ epsilon0_smpaxi*mat1_epsilonrS_2_3_ epsilon0_smpaxi*mat1_epsilonrS_3_3_ mat1_cE_1_1_ mat1_cE_1_2_ mat1_cE_1_3_ mat1_cE_1_4_ mat1_cE_1_5_ mat1_cE_1_6_ mat1_cE_2_2_ mat1_cE_2_3_ mat1_cE_2_4_ mat1_cE_2_5_ mat1_cE_2_6_ mat1_cE_3_3_ mat1_cE_3_4_ mat1_cE_3_5_ mat1_cE_3_6_ mat1_cE_4_4_ mat1_cE_4_5_ mat1_cE_4_6_ mat1_cE_5_5_ mat1_cE_5_6_ mat1_cE_6_6_ E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 0.5*E_smpaxi/(1+nu_smpaxi) 0 0 0.5*E_smpaxi/(1+nu_smpaxi) 0 0.5*E_smpaxi/(1+nu_smpaxi) D11_smpaxi*er_smpaxi+D12_smpaxi*ephi_smpaxi+D13_smpaxi*ez_smpaxi cE11_smpaxi*er_smpaxi+cE12_smpaxi*ephi_smpaxi+cE13_smpaxi*ez_smpaxi+2*cE15_smpaxi*erz_smpaxi-e11_smpaxi*Er_smpaxi-e31_smpaxi*Ez_smpaxi D12_smpaxi*er_smpaxi+D22_smpaxi*ephi_smpaxi+D23_smpaxi*ez_smpaxi cE12_smpaxi*er_smpaxi+cE22_smpaxi*ephi_smpaxi+cE23_smpaxi*ez_smpaxi+2*cE25_smpaxi*erz_smpaxi-e12_smpaxi*Er_smpaxi-e32_smpaxi*Ez_smpaxi D13_smpaxi*er_smpaxi+D23_smpaxi*ephi_smpaxi+D33_smpaxi*ez_smpaxi cE13_smpaxi*er_smpaxi+cE23_smpaxi*ephi_smpaxi+cE33_smpaxi*ez_smpaxi+2*cE35_smpaxi*erz_smpaxi-e13_smpaxi*Er_smpaxi-e33_smpaxi*Ez_smpaxi 2*D66_smpaxi*erz_smpaxi cE15_smpaxi*er_smpaxi+cE25_smpaxi*ephi_smpaxi+cE35_smpaxi*ez_smpaxi+2*cE55_smpaxi*erz_smpaxi-e15_smpaxi*Er_smpaxi-e35_smpaxi*Ez_smpaxi e11_smpaxi*er_smpaxi+e12_smpaxi*ephi_smpaxi+e13_smpaxi*ez_smpaxi+2*e15_smpaxi*erz_smpaxi+epsilonSrr_smpaxi*Er_smpaxi+epsilonSrz_smpaxi*Ez_smpaxi e31_smpaxi*er_smpaxi+e32_smpaxi*ephi_smpaxi+e33_smpaxi*ez_smpaxi+2*e35_smpaxi*erz_smpaxi+epsilonSrz_smpaxi*Er_smpaxi+epsilonSzz_smpaxi*Ez_smpaxi -Vr -Vz -(sr_smpaxi+sphi_smpaxi+sz_smpaxi)/3 uorz*r-wr 0.5*(sr_smpaxi*er_smpaxi+sphi_smpaxi*ephi_smpaxi+sz_smpaxi*ez_smpaxi+2*srz_smpaxi*erz_smpaxi) sqrt(sr_smpaxi^2+sphi_smpaxi^2+sz_smpaxi^2-sr_smpaxi*sphi_smpaxi-sphi_smpaxi*sz_smpaxi-sr_smpaxi*sz_smpaxi+3*srz_smpaxi^2) max(max(abs(s1_smpaxi-s2_smpaxi),abs(s2_smpaxi-s3_smpaxi)),abs(s1_smpaxi-s3_smpaxi)) 0.5*(Er_smpaxi*Dr_smpaxi+Ez_smpaxi*Dz_smpaxi) sqrt(abs(Er_smpaxi)^2+abs(Ez_smpaxi)^2) sqrt(abs(Dr_smpaxi)^2+abs(Dz_smpaxi)^2) Ws_smpaxi We_smpaxi+Ws_smpaxi uorr*r+uor uor wz 0.5*(uorz*r+wr) sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 254650000000 200000000000 0 0.33 7500 mat1_rho 1 59900000 0 xz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 {0,0} {0,0} {1,2} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"-r*uor","-w","0"} {"0","0","0"} {"0","0","V0_smpaxi-V"} {"-r*uor","-w","-V"} {"0","0","0"} {"test(-r*uor)","test(-w)","0"} {"0","0","0"} {"0","0","test(V0_smpaxi-V)"} {"test(-r*uor)","test(-w)","test(-V)"} 12 12 123 123 123 1 111 111 111 111 111 111 111 111 111 111 111 111 111 111 111 {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"uor","w","V"} sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 sr_smpaxi*nr_smpaxi+srz_smpaxi*nz_smpaxi srz_smpaxi*nr_smpaxi+sz_smpaxi*nz_smpaxi unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) 0 0 0 0 0 0 0 0 0 0 0 0 UP 100 0 0 0 0 nr nz 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 {0,0,0,0,0,0,0} {0,0,0,0,0,0,0} {1,2,3,4,5,1,3} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} 12 123 1 111 111 {"","",""} {"","",""} {"","",""} {"","",""} {"uor","w","V"} sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 0 0 0 0 0 0 0 0 0 0 {0,0,0,0,0,0} {0,0,0,0,0,0} {1,2,2,1,2,2} Wes_tot_smpaxi 8.854187817000001e-012 Wes_tot_g1_smpaxi elpric {"1"} {"real(sr_smpaxi)","0","real(sphi_smpaxi)","real(srz_smpaxi)","0","rt�`eal(sz_smpaxi)"} {"1","2"} s smpaxi {"r","phi","z"} elpric {"1"} {"real(er_smpaxi)","0","real(ephi_smpaxi)","real(erz_smpaxi)","0","real(ez_smpaxi)"} {"1","2"} e smpaxi {"r","phi","z"} elcplscalar {"1"} 2*pi*r*Wes_smpaxi ref 4 {"1","2"} {"Wes_tot_g1_smpaxi"} {"1"} elcplscalar {"1"} ref {"3","6"} {"1","2","4","5"} {"dis1"} {"1"} {}

{"R1","R2"}
{0} {0} smpaxi weak Lead Zirconate Titanate (PZT-2) mat1 7600[kg/m^3] {"990","0","0"} {"990","0"} {"450"} {"0[C/N]","0[C/N]","0[C/N]","0[C/N]","4.4e-010[C/N]","0[C/N]"} {"0[C/N]","0[C/N]","0[C/N]","4.4e-010[C/N]","0[C/N]","0[C/N]"} {"-6e-011[C/N]","-6e-011[C/N]","1.52e-010[C/N]","0[C/N]","0[C/N]","0[C/N]"} {"0[C/m^2]","0[C/m^2]","0[C/m^2]","0[C/m^2]","9.77778[C/m^2]","0[C/m^2]"} {"0[C/m^2]","0[C/m^2]","0[C/m^2]","9.77778[C/m^2]","0[C/m^2]","0[C/m^2]"} {"-1.81603[C/m^2]","-1.81603[C/m^2]","9.05058[C/m^2]","0[C/m^2]","0[C/m^2]","0[C/m^2]"} {"504.1","0","0"} {"504.1","0"} {"270"} {"1.16e-011[1/Pa]","-3.33e-012[1/Pa]","-4.97e-012[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"1.16e-011[1/Pa]","-4.97e-012[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"1.48e-011[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"4.5e-011[1/Pa]","0[1/Pa]","0[1/Pa]"} {"4.5e-011[1/Pa]","0[1/Pa]"} {"2.99e-011[1/Pa]"} {"1.34868e+011[Pa]","6.78883e+010[Pa]","6.80876e+010[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"1.34868e+011[Pa]","6.80876e+010[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"1.13297e+011[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"2.22222e+010[Pa]","0[Pa]","0[Pa]"} {"2.22222e+010[Pa]","0[Pa]"} {"3.34448e+010[Pa]"} Alumina mat2 900[J/(kg*K)] 300e9[Pa] 8e-6[1/K] 27[W/(m*K)] 0.222 3900[kg/m^3] Resistivity {"alphares","T0","res0"} {"Temperature coefficient","Reference temperature","Resistivity at reference temperature"} SI
COMSOL 3.5 a 0 608 $Name: v35ap $ $Date: 2009/05/11 07:38:49 $ 2 geom on on off on on off on 0.1 t PiezoAxialSym axi {"uor","w","V"} {"r","phi","z"} smpaxi SME {"shlag(2,'uor')","shlag(2,'w')","shlag(2,'V')"} 4 2 2 on _smpaxi ephii_smpaxi eri_smpaxi erzi_smpaxi ezi_smpaxi sphii_smpaxi sri_smpaxi srzi_smpaxi szi_smpaxi Lag2 static freq symmetric_es off ref defined_by_structural_frame defined_by_structural_frame off {"lm1","lm2","lm3"} ideal 0 0 global global 0
0 0 0 0 0 0 {1,1,1,1,1,1}
0 0 global global 0
0 0 0 free axisym fixed fixed axisym free 0 0 0 0 0 0 0 0 nD0 ax V0 nD0 nD0 V 0 {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} 0 0 100 0 0 UP {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} {"0","0"} 0 0 0 0 {5,4,2,6,3,1,1}
123 123 111 111 111 111 {"0","0","0"} {"0","0","0"} 1 iso piezoelectric global stress 1 0 2.5465E11 2.0e11 0 0.33 7500 mat1_rho {"0","0","0"} {"0","0","0"} {"16.5e-12","-4.78e-12","-8.45e-12","0","0","0","-4.78e-12","16.5e-12","-8.45e-12","0","0","0","-8.45e-12","-8.45e-12","20.7e-12","0","0","0","0","0","0","43.5e-12","0","0","0","0","0","0","43.5e-12","0","0","0","0","0","0","42.6e-12"} {"mat1_sE_1_1_","mat1_sE_2_1_","mat1_sE_3_1_","mat1_sE_4_1_","mat1_sE_5_1_","mat1_sE_6_1_","mat1_sE_1_2_","mat1_sE_2_2_","mat1_sE_3_2_","mat1_sE_4_2_","mat1_sE_5_2_","mat1_sE_6_2_","mat1_sE_1_3_","mat1_sE_2_3_","mat1_sE_3_3_","mat1_sE_4_3_","mat1_sE_5_3_","mat1_sE_6_3_","mat1_sE_1_4_","mat1_sE_2_4_","mat1_sE_3_4_","mat1_sE_4_4_","mat1_sE_5_4_","mat1_sE_6_4_","mat1_sE_1_5_","mat1_sE_2_5_","mat1_sE_3_5_","mat1_sE_4_5_","mat1_sE_5_5_","mat1_sE_6_5_","mat1_sE_1_6_","mat1_sE_2_6_","mat1_sE_3_6_","mat1_sE_4_6_","mat1_sE_5_6_","mat1_sE_6_6_"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"mat1_cE_1_1_","mat1_cE_2_1_","mat1_cE_3_1_","mat1_cE_4_1_","mat1_cE_5_1_","mat1_cE_6_1_","mat1_cE_1_2_","mat1_cE_2_2_","mat1_cE_3_2_","mat1_cE_4_2_","mat1_cE_5_2_","mat1_cE_6_2_","mat1_cE_1_3_","mat1_cE_2_3_","mat1_cE_3_3_","mat1_cE_4_3_","mat1_cE_5_3_","mat1_cE_6_3_","mat1_cE_1_4_","mat1_cE_2_4_","mat1_cE_3_4_","mat1_cE_4_4_","mat1_cE_5_4_","mat1_cE_6_4_","mat1_cE_1_5_","mat1_cE_2_5_","mat1_cE_3_5_","mat1_cE_4_5_","mat1_cE_5_5_","mat1_cE_6_5_","mat1_cE_1_6_","mat1_cE_2_6_","mat1_cE_3_6_","mat1_cE_4_6_","mat1_cE_5_6_","mat1_cE_6_6_"} {"0","0","-274e-12","0","0","-274e-12","0","0","593e-12","0","741e-12","0","741e-12","0","0","0","0","0"} {"mat1_d_1_1_","mat1_d_2_1_","mat1_d_3_1_","mat1_d_1_2_","mat1_d_2_2_","mat1_d_3_2_","mat1_d_1_3_","mat1_d_2_3_","mat1_d_3_3_","mat1_d_1_4_","mat1_d_2_4_","mat1_d_3_4_","mat1_d_1_5_","mat1_d_2_5_","mat1_d_3_5_","mat1_d_1_6_","mat1_d_2_6_","mat1_d_3_6_"} {"0","0","-6.62281","0","0","-6.62281","0","0","23.2403","0","17.0345","0","17.0345","0","0","0","0","0"} {"mat1_e_1_1_","mat1_e_2_1_","mat1_e_3_1_","mat1_e_1_2_","mat1_e_2_2_","mat1_e_3_2_","mat1_e_1_3_","mat1_e_2_3_","mat1_e_3_3_","mat1_e_1_4_","mat1_e_2_4_","mat1_e_3_4_","mat1_e_1_5_","mat1_e_2_5_","mat1_e_3_5_","mat1_e_1_6_","mat1_e_2_6_","mat1_e_3_6_"} {"3130","0","0","0","3130","0","0","0","3400"} {"mat1_epsilonrT_1_1_","mat1_epsilonrT_2_1_","mat1_epsilonrT_3_1_","mat1_epsilonrT_1_2_","mat1_epsilonrT_2_2_","mat1_epsilonrT_3_2_","mat1_epsilonrT_1_3_","mat1_epsilonrT_2_3_","mat1_epsilonrT_3_3_"} {"1704.40","0","0","0","1704.40","0","0","0","1433.61"} {"mat1_epsilonrS_1_1_","mat1_epsilonrS_2_1_","mat1_epsilonrS_3_1_","mat1_epsilonrS_1_2_","mat1_epsilonrS_2_2_","mat1_epsilonrS_3_2_","mat1_epsilonrS_1_3_","mat1_epsilonrS_2_3_","mat1_epsilonrS_3_3_"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"1.27205e11","8.02122e10","8.46702e10","0","0","0","8.02122e10","1.27205e11","8.46702e10","0","0","0","8.46702e10","8.46702e10","1.17436e11","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.29886e10","0","0","0","0","0","0","2.34742e10"} {"1","0","0","0","1","0","0","0","1"} {"1","0","0","0","1","0","0","0","1"} {"5.99e7","0","0","0","5.99e7","0","0","0","5.99e7"} {"5.99e7","0","0","0","5.99e7","0","0","0","5.99e7"} 1 5.99e7 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 xz nodamping 0 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} 0 0 {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"} 0 {"0","0","0","0","0","0","0","0","0"} {"0","0","0","0","0","0","0","0","0"} noloss noloss 0 0 global global 0
0 0 0 free 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 {"0","0"} {"0","0"} {1,2}
Wes_tot_smpaxi 8.854187817e-12
{"r","z"} {"ref"} {"shlag(2,'uor')","shlag(2,'w')","shlag(2,'V')"} 4 2 2 on 1
weak
SI {"0","0","0"} 111 {1,1} 12 123 111 111 111 111 {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"-(test(er_smpaxi)*sr_smpaxi+test(ephi_smpaxi)*sphi_smpaxi+test(ez_smpaxi)*sz_smpaxi+2*test(erz_smpaxi)*srz_smpaxi)*r","0","0"} {"-(test(er_smpaxi)*sr_smpaxi+test(ephi_smpaxi)*sphi_smpaxi+test(ez_smpaxi)*sz_smpaxi+2*test(erz_smpaxi)*srz_smpaxi)*r","0","r*(Dr_smpaxi*test(Er_smpaxi)+Dz_smpaxi*test(Ez_smpaxi))"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} 1 111 111 {"uor","w","V"} mat1_e_1_1_ mat1_e_1_2_ mat1_e_1_3_ mat1_e_1_4_ mat1_e_1_5_ mat1_e_1_6_ mat1_e_2_1_ mat1_e_2_2_ mat1_e_2_3_ mat1_e_2_4_ mat1_e_2_5_ mat1_e_2_6_ mat1_e_3_1_ mat1_e_3_2_ mat1_e_3_3_ mat1_e_3_4_ mat1_e_3_5_ mat1_e_3_6_ epsilon0_smpaxi*mat1_epsilonrS_1_1_ epsilon0_smpaxi*mat1_epsilonrS_1_2_ epsilon0_smpaxi*mat1_epsilonrS_1_3_ epsilon0_smpaxi*mat1_epsilonrS_2_2_ epsilon0_smpaxi*mat1_epsilonrS_2_3_ epsilon0_smpaxi*mat1_epsilonrS_3_3_ mat1_cE_1_1_ mat1_cE_1_2_ mat1_cE_1_3_ mat1_cE_1_4_ mat1_cE_1_5_ mat1_cE_1_6_ mat1_cE_2_2_ mat1_cE_2_3_ mat1_cE_2_4_ mat1_cE_2_5_ mat1_cE_2_6_ mat1_cE_3_3_ mat1_cE_3_4_ mat1_cE_3_5_ mat1_cE_3_6_ mat1_cE_4_4_ mat1_cE_4_5_ mat1_cE_4_6_ mat1_cE_5_5_ mat1_cE_5_6_ mat1_cE_6_6_ E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) E_smpaxi*nu_smpaxi/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 E_smpaxi*(1-nu_smpaxi)/((1+nu_smpaxi)*(1-2*nu_smpaxi)) 0 0 0 0.5*E_smpaxi/(1+nu_smpaxi) 0 0 0.5*E_smpaxi/(1+nu_smpaxi) 0 0.5*E_smpaxi/(1+nu_smpaxi) D11_smpaxi*er_smpaxi+D12_smpaxi*ephi_smpaxi+D13_smpaxi*ez_smpaxi cE11_smpaxi*er_smpaxi+cE12_smpaxi*ephi_smpaxi+cE13_smpaxi*ez_smpaxi+2*cE15_smpaxi*erz_smpaxi-e11_smpaxi*Er_smpaxi-e31_smpaxi*Ez_smpaxi D12_smpaxi*er_smpaxi+D22_smpaxi*ephi_smpaxi+D23_smpaxi*ez_smpaxi cE12_smpaxi*er_smpaxi+cE22_smpaxi*ephi_smpaxi+cE23_smpaxi*ez_smpaxi+2*cE25_smpaxi*erz_smpaxi-e12_smpaxi*Er_smpaxi-e32_smpaxi*Ez_smpaxi D13_smpaxi*er_smpaxi+D23_smpaxi*ephi_smpaxi+D33_smpaxi*ez_smpaxi cE13_smpaxi*er_smpaxi+cE23_smpaxi*ephi_smpaxi+cE33_smpaxi*ez_smpaxi+2*cE35_smpaxi*erz_smpaxi-e13_smpaxi*Er_smpaxi-e33_smpaxi*Ez_smpaxi 2*D66_smpaxi*erz_smpaxi cE15_smpaxi*er_smpaxi+cE25_smpaxi*ephi_smpaxi+cE35_smpaxi*ez_smpaxi+2*cE55_smpaxi*erz_smpaxi-e15_smpaxi*Er_smpaxi-e35_smpaxi*Ez_smpaxi e11_smpaxi*er_smpaxi+e12_smpaxi*ephi_smpaxi+e13_smpaxi*ez_smpaxi+2*e15_smpaxi*erz_smpaxi+epsilonSrr_smpaxi*Er_smpaxi+epsilonSrz_smpaxi*Ez_smpaxi e31_smpaxi*er_smpaxi+e32_smpaxi*ephi_smpaxi+e33_smpaxi*ez_smpaxi+2*e35_smpaxi*erz_smpaxi+epsilonSrz_smpaxi*Er_smpaxi+epsilonSzz_smpaxi*Ez_smpaxi -Vr -Vz -(sr_smpaxi+sphi_smpaxi+sz_smpaxi)/3 uorz*r-wr 0.5*(sr_smpaxi*er_smpaxi+sphi_smpaxi*ephi_smpaxi+sz_smpaxi*ez_smpaxi+2*srz_smpaxi*erz_smpaxi) sqrt(sr_smpaxi^2+sphi_smpaxi^2+sz_smpaxi^2-sr_smpaxi*sphi_smpaxi-sphi_smpaxi*sz_smpaxi-sr_smpaxi*sz_smpaxi+3*srz_smpaxi^2) max(max(abs(s1_smpaxi-s2_smpaxi),abs(s2_smpaxi-s3_smpaxi)),abs(s1_smpaxi-s3_smpaxi)) 0.5*(Er_smpaxi*Dr_smpaxi+Ez_smpaxi*Dz_smpaxi) sqrt(abs(Er_smpaxi)^2+abs(Ez_smpaxi)^2) sqrt(abs(Dr_smpaxi)^2+abs(Dz_smpaxi)^2) Ws_smpaxi We_smpaxi+Ws_smpaxi uorr*r+uor uor wz 0.5*(uorz*r+wr) sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 254650000000 200000000000 0 0.33 7500 mat1_rho 1 59900000 0 xz 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 {0,0} {0,0} {1,2} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"-r*uor","-w","0"} {"0","0","0"} {"0","0","V0_smpaxi-V"} {"-r*uor","-w","-V"} {"0","0","0"} {"test(-r*uor)","test(-w)","0"} {"0","0","0"} {"0","0","test(V0_smpaxi-V)"} {"test(-r*uor)","test(-w)","test(-V)"} 12 12 123 123 123 1 111 111 111 111 111 111 111 111 111 111 111 111 111 111 111 {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"","",""} {"uor","w","V"} sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 sr_smpaxi*nr_smpaxi+srz_smpaxi*nz_smpaxi srz_smpaxi*nr_smpaxi+sz_smpaxi*nz_smpaxi unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) unr*(Dr_smpaxi_down-Dr_smpaxi_up)+unz*(Dz_smpaxi_down-Dz_smpaxi_up) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unr+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unr+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Er_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(up(Er_smpaxi)*up(Dr_smpaxi)+up(Ez_smpaxi)*up(Dz_smpaxi))*unz+(dnr*up(Dr_smpaxi)+dnz*up(Dz_smpaxi))*up(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) -0.5*(down(Er_smpaxi)*down(Dr_smpaxi)+down(Ez_smpaxi)*down(Dz_smpaxi))*unz+(unr*down(Dr_smpaxi)+unz*down(Dz_smpaxi))*down(Ez_smpaxi) 0 0 0 0 0 0 0 0 0 0 0 0 UP 100 0 0 0 0 nr nz 0 1 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 {0,0,0,0,0,0,0} {0,0,0,0,0,0,0} {1,2,3,4,5,1,3} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} {"0","0","0"} 12 123 1 111 111 {"","",""} {"","",""} {"","",""} {"","",""} {"uor","w","V"} sqrt(real(uaxi_smpaxi)^2+real(w)^2) uor*r uorr*r+uor uorz*r 0 0 0 0 0 0 0 0 0 0 0 0 {0,0,0,0,0,0} {0,0,0,0,0,0} {1,2,2,1,2,2} Wes_tot_smpaxi 8.854187817000001e-012 Wes_tot_g1_smpaxi elpric {"1"} {"real(sr_smpaxi)","0","real(sphi_smpaxi)","real(srz_smpaxi)","0","real(sz_smpaxi)"} {"1","2"} s smpaxi {"r","phi","z"} elpric {"1"} {"real(er_smpaxi)","0","real(ephi_smpaxi)","real(erz_smpaxi)","0","real(ez_smpaxi)"} {"1","2"} e smpaxi {"r","phi","z"} elcplscalar {"1"} 2*pi*r*Wes_smpaxi ref 4 {"1","2"} {"Wes_tot_g1_smpaxi"} {"1"} elcplscalar {"1"} ref {"3","6"} {"1","2","4","5"} {"dis1"} {"1"} {}

{0} {0} smpaxi weak Lead Zirconate Titanate (PZT-2) mat1 7600[kg/m^3] {"990","0","0"} {"990","0"} {"450"} {"0[C/N]","0[C/N]","0[C/N]","0[C/N]","4.4e-010[C/N]","0[C/N]"} {"0[C/N]","0[C/N]","0[C/N]","4.4e-010[C/N]","0[C/N]","0[C/N]"} {"-6e-011[C/N]","-6e-011[C/N]","1.52e-010[C/N]","0[C/N]","0[C/N]","0[C/N]"} {"0[C/m^2]","0[C/m^2]","0[C/m^2]","0[C/m^2]","9.77778[C/m^2]","0[C/m^2]"} {"0[C/m^2]","0[C/m^2]","0[C/m^2]","9.77778[C/m^2]","0[C/m^2]","0[C/m^2]"} {"-1.81603[C/m^2]","-1.81603[C/m^2]","9.05058[C/m^2]","0[C/m^2]","0[C/m^2]","0[C/m^2]"} {"504.1","0","0"} {"504.1","0"} {"270"} {"1.16e-011[1/Pa]","-3.33e-012[1/Pa]","-4.97e-012[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"1.16e-011[1/Pa]","-4.97e-012[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"1.48e-011[1/Pa]","0[1/Pa]","0[1/Pa]","0[1/Pa]"} {"4.5e-011[1/Pa]","0[1/Pa]","0[1/Pa]"} {"4.5e-011[1/Pa]","0[1/Pa]"} {"2.99e-011[1/Pa]"} {"1.34868e+011[Pa]","6.78883e+010[Pa]","6.80876e+010[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"1.34868e+011[Pa]","6.80876e+010[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"1.13297e+011[Pa]","0[Pa]","0[Pa]","0[Pa]"} {"2.22222e+010[Pa]","0[Pa]","0[Pa]"} {"2.22222e+010[Pa]","0[Pa]"} {"3.34448e+010[Pa]"} Alumina mat2 900[J/(kg*K)] 300e9[Pa] 8e-6[1/K] 27[W/(m*K)] 0.222 3900[kg/m^3] Resistivity {"alphares","T0","res0"} {"Temperature coefficient","Reference temperature","Resistivity at reference temperature"} SI
uq~ t�� off parametric parametric auto 1.0E-6 25 tol 100 1 off on off 1.0 1.0E-4 10.0 off on 0.0010 25 lumped automatic auto on 1 4 tol 10 1 off const 1.0 minimal 1.0 1.0E-2 10.0 0.0010 0.01 range(0,0.1,1) 0 1 0.1 11 step none tlist free bdf_ida 0.01 off 15 off on on on on on on off on on 0.0010 5 1 0.1 0.75 linear off off maybe bweuler 0 off 6 0 300 0.0 0 lambda 0 UP range(100,100,300) 100 300 100 step none off 1 off 0.0 0.0 0.0 on auto auto auto eliminate auto 1000 on auto on off off on off currgeom l2 10000000 longest weak on 0 1 2 1 fltpft 2 1.7 0.5 0.5 on off off sensitivity adjoint on cholesky analytic 500 10 1.0e-6 1.0e-6 1.0e-6 1.0e-6 0 off w,V,uor w,V,uor on init_expr_currsol_radio Automatic 0 u_init_radio Automatic 0 off off off off umfpack linsolver 0.0 0.1 0.7 nd on off nd on 1.0E-8 on off tol 2 1.0E-6 400.0 10000 left right 1 50 1 1.0 3 6 v 5000 512.0 off 2.0 on droptol gmres 0.02 100 0.8 on uncoupled 1.0 on on shape regular on 2 2 off Geom1 on on uor w V 1e-3 1 umfpack linsolver 0.0 0.1 0.7 nd on off nd on 1.0E-8 on off tol 2 1.0E-6 400.0 10000 left right 1 50 1 1.0 3 6 v 5000 512.0 off 2.0 on droptol gmres 0.02 100 0.8 on uncoupled 1.0 on on shape regular on 2 2 off Geom1 on on 1 iter 0.5 1 1 20 10 1.0E-2 1 const off 1.0 1.0E-4 1.0E-2 10.0 minimal onevery off off off auto on umfpack gmg auto on umfpack gmg Probe 1 interp Geom1 {"disp_smpaxi"} off {"0","0"} step none step none 0 on on on {"lin","lin"} on 0 1 0 1 off Geom1 0 off off off 1029014 COMSOL 3.5.0.608 1263477603289 1259858204046 off html off a4 off full off Geom1 draw 0 -0.053339 0.073339 -0.042407495867768596 0.02808549586776859 -1.0 1.0 0.0050 0.0050 0.01 -6.333900000000002 6.333900000000002 -3.686274158125916 3.686274158125916 1.0 -0.7161 63.339 1.0 -0.7161 0.0 0.0 1.0 0.0 point headlight on 255 255 255 1.0 -0.7161 63.339 directional light 1 on 255 255 255 1.0 -1.0 1.0 directional light 2 on 255 255 255 -1.0 1.0 -1.0 directional light 3 on 255 255 255 -1.0 -1.0 1.0 directional light 4 on 255 255 255 1.0 -1.0 -1.0 on on on on off on on on off on on on off off off off 1.0 1.0 1.0 size cycle off off 0.5 orbit none none off off off off on off off on on on on on on 1.0E-6 intersection 1.0 normal off 2 100.0 off on off on off off on on 5 on 1 0.3 1.3 0.001 1 10 1.0 1.0 on 0 regular {"","","","","",""} {"","","","","",""} {"","","","","","",""} {"","","","","","",""} {"","","","","","",""} {"","","","","","",""} {"",""} {"triaf","triaf"} {"",""} on {"w"} on -1.8031960927107342E-8 0.0 on off m {"disp_smpaxi"} off nm GrayPrint off on on 255,0,0 interp fill off {"disp_smpaxi"} on off m {"disp_smpaxi"} off m {"disp_smpaxi"} on off m Rainbow off on on 255,0,0 20 off off step none off off {"disp_smpaxi"} on 0.0 4.698042957948526E-8 on off m {"disp_smpaxi"} off m Rainbow off on on 255,0,0 interp off sub {"uaxi_smpaxi","w"} off m {"uaxi_smpaxi","w"} off m {"disp_smpaxi"} off m 15 off 15 off step none step none arrow proportional 255,0,0 on 1 off {"s1_smpaxi","s1r_smpaxi","s1phi_smpaxi","s1z_smpaxi","s2_smpaxi","s2r_smpaxi","s2phi_smpaxi","s2z_smpaxi","s3_smpaxi","s3r_smpaxi","s3phi_smpaxi","s3z_smpaxi"} off Pa {"disp_smpaxi"} off m 8 off 8 off step none step none arrow proportional 0,153,0 on 1 off {"uaxi_smpaxi","w"} m off 255,0,0 {"disp_smpaxi"} m Rainbow off on {"disp_smpaxi"} off m 20 sub off step none step none 0.001 0.01 0.01 Inf 5000 on off 0.05 20 off 1 0.5 1.3 0.5 none off mass lines 1 {"","",""} {"uaxi_smpaxi","w"} m on {"0","0","0"} partstart_explicit 10 off step none {"0","0"} step none step none off 255,0,0 {"disp_smpaxi"} m Rainbow off on 255,0,0 on 1 once step none stick 0.001 off {""} {""} off on on 0.001 partt off 5 0.001 off {"",""} {"",""} off on on 0.001 {"partu","partv","partw"} partt off 5 off {"disp_smpaxi"} off on m {"disp_smpaxi"} off off m off off on 6 {"Geom1"} 0 2 stored step none on on off all on off on on on {"uaxi_smpaxi","w"} m {"uaxi_smpaxi","w"} m off 100000 0,1,2 stored step none moviefile AVI 640 480 10 full 11 off off off {"uaxi_smpaxi"} off m 0 2 stored step none on auto 4 on {"Fzg_smpaxi"} off N/m 0 2 stored step none off auto 4 on {"disp_smpaxi"} off m^3 0 2 stored step none {"disp_smpaxi"} on on off m Rainbow off on on 255,0,0 interp fill off {"disp_smpaxi"} on off m arc off {"disp_smpaxi"} m solid cyclecolor none off off 255,0,0 Rainbow off on on 255,0,0 interp fill {"disp_smpaxi"} off m off {"disp_smpaxi"} m solid cyclecolor none off off 255,0,0 255,0,0 0 0,1,2 stored step none on on on {"lin","lin"} on on 1 0 off {"w"} off nm arc off {"disp_smpaxi"} m solid cyclecolor none off off 255,0,0 Rainbow off on on 255,0,0 interp fill 200 {"0.001","0.001","0","-0.04"} 5 off off step none {"disp_smpaxi"} off m off {"disp_smpaxi"} m^3 solid cyclecolor none off off 255,0,0 {"0","0"} step none step none 255,0,0 0 0,1,2 stored step none on on on {"lin","lin"} on 0 {"disp_smpaxi"} off m element 2 {"disp_smpaxi"} off off m element 2 {"disp_smpaxi"} off off m 10 off 10 off step none step none element 2 0 0,1,2 stored step none on ptd off 2 coorddata C:\Users\cwalter.EMCE\Desktop\test.m on off on 0 2 stored step none step none {"disp_smpaxi"} off m {"0","0"} {} {} off solid cyclecolor none off off 255,0,0 on on on {"lin","lin"} 0 0,1,2 stored step none 0 0,1,0,0,0,1,0,0,0 0,1,0,0,0,0,1,0,0,0,0,1 Geom1 10 0 up on off 128,128,128 off on 192,192,192 on 0,0,0 off all 1 random Rainbow off on uq~ srcom.femlab.geom.Rect�ȉ,E��6DlxDlyLlxExprt!Lcom/femlab/geom/Geom$Expression;LlyExprq~.xrcom.femlab.geom.Prim2�Z��~��DrotLbaseq~Lconstrq~[post[D[posExprt"[Lcom/femlab/geom/Geom$Expression;LrotExprq~.xrcom.femlab.geom.Geom2�V���c/Oxrcom.femlab.geom.Geom͹�6��{L geomAssoctLcom/femlab/geom/GeomAssoc;Lversionq~xpwsq~wq~q~t#COMSOL Reaction Engineering Lab 3.5tat COMSOL 3.5q~8w`t$Name: v35ap $t$Date: 2009/05/11 07:38:49 $xw`uq~#`Geom2�����|�=-C��6?{�G�z�������{�G�zt?{�G�z�������{�G�zt?�����������?��?��?��?� BezierCurve{�G�z���?{�G�zt?{�G�z���? 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