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  • 2020-11-27 11:41
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matlab程序。模拟形状记忆合金的形状记忆效应。
SMA_Spring2.rar
  • SMA_Spring2.m
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内容介绍
clc clear format long EA=67.0*10^3; EM=26.3*10^3; Theta=0.55; Mf=9; Ms=18.4; As=34.5; Af=49; CM=8; CA=13.8; sigmacrs=100; sigmacrf=170; epsilonL=0.067; aA=pi/(Af-As); aM=pi/(Ms-Mf); bA=-aA/CA; bM=-aM/CM; Area_SMA=0.01;%mm^2 Length_SMA=500;%%mm E_cable=0.5e20; A_cable=3.1415926*1.4*1.4/4; L_cable=500; k1=E_cable*A_cable/L_cable; k2=k1; epsilon0=0.005;%0.005 T0=20;%初始温度 sigma0=128; xis0=0.046; xiT0=0; xi0=xis0+xiT0;%%初始马氏体体积分数 Exi0=EA+xi0*(EM-EA); omegaxi0=-epsilonL*Exi0; Mcofxi0=1/(1+Exi0*Area_SMA/Length_SMA*(1/k1+1/k2)); tic Num_division1=30; Num_division2=30; xis1=xis0; xiT1=xiT0; xi1=xi0; Exi1=Exi0; omegaxi1=omegaxi0; Mcofxi1=Mcofxi0; Asigmas=(aA*As-bA*sigma0+bA*Mcofxi1*Theta*T0)/(aA+Mcofxi1*Theta*bA); sigma1=Mcofxi1*Theta*(Asigmas-T0)+sigma0; xi2=0; xis2=xis1-xis1/xi1*(xi1-xi2); xiT2=xiT1-xiT1/xi1*(xi1-xi2); Exi2=EA+xi2*(EM-EA); omegaxi2=-epsilonL*Exi2; Mcofxi2=1/(1+Exi2*Area_SMA/Length_SMA*(1/k1+1/k2)); epsilon1=epsilon0-(sigma1-sigma0)*(Area_SMA/Length_SMA*(1/k1+1/k2)); AAA1=(-bA*Exi2*epsilon1+bA*Exi1*epsilon1-bA*omegaxi2*xis2+bA*omegaxi1*xis1+bA*Theta*Asigmas); Asigmaf=(aA*As-bA*sigma1+Mcofxi2*(-bA*Exi2*epsilon1+bA*Exi1*epsilon1-bA*omegaxi2*xis2+bA*omegaxi1*xis1+bA*Theta*Asigmas)+pi)/(aA+bA*Mcofxi2*Theta); sigma2=(pi-aA*(Asigmaf-As))/bA; xi3=xi2; xis3=xis2; xiT3=xiT2; Exi3=Exi2; omegaxi3=omegaxi2; Mcofxi3=Mcofxi2; epsilon2=epsilon1-(sigma2-sigma1)*(Area_SMA/Length_SMA*(1/k1+1/k2)); Msigmas=(sigma2-sigmacrs+CM*Ms-Mcofxi3*Theta*Asigmaf)/(CM-Mcofxi3*Theta); sigma3=sigma2+Mcofxi3*Theta*(Msigmas-Asigmaf); xi4=xi0; xis4=xis0; xiT4=xiT0; Exi4=Exi0; omegaxi4=omegaxi0; Mcofxi4=1/(1+Exi4*Area_SMA/Length_SMA*(1/k1+1/k2)); epsilon3=epsilon2-(sigma3-sigma2)*(Area_SMA/Length_SMA*(1/k1+1/k2)); Msigmaf=(sigma3-sigmacrf+Mcofxi4*(Exi4*epsilon3-Exi3*epsilon3+omegaxi4*xis4-omegaxi3*xis3-Theta*Msigmas)+CM*Ms+(sigmacrf-sigmacrs)/pi*acos((2*xis4-xis3-1)/(1-xis3)))/(CM-Mcofxi4*Theta); T4_1=Msigmaf; sigma4=sigma3+Mcofxi4*(Exi4*epsilon3-Exi3*epsilon3+Theta*(Msigmaf-Msigmas)+omegaxi4*xis4-omegaxi3*xis3); sigma4_test=Mcofxi0*Theta*(Msigmaf-T0)+sigma0; xis4_test=(1-xis3)/2*cos(pi/(sigmacrf-sigmacrs)*(sigma4-sigmacrf-CM*(Msigmaf-Ms)))+(1+xis3)/2; epsilon4=epsilon3-(sigma4-sigma3)*(Area_SMA/Length_SMA*(1/k1+1/k2)); figure(1) T_1=linspace(T0,Asigmas,Num_division1); Mcofxi=Mcofxi0; sigmar_1=Mcofxi*Theta*(T_1-T0)+sigma0; xi01=xi0+T_1-T_1; yu01=epsilon0-(1/Mcofxi-1)*(sigmar_1-sigma0)/Exi1; syms T sigma xi=xi1/2*(cos(aA*(T-As-sigma/CA))+1); xis=xis1-xis1/xi1*(xi1-xi); Exi=EA+xi*(EM-EA); omegaxi=-epsilonL*Exi; Mcofxi=1/(1+Exi*Area_SMA/Length_SMA*(1/k1+1/k2)); F=Mcofxi*(Exi*epsilon1-Exi1*epsilon1+omegaxi*xis-omegaxi1*xis1+Theta*(T-Asigmas))+sigma1-sigma;%%--- dF=diff(F,sigma); sigma=sigma1+1; i=1; for T=linspace(Asigmas,Asigmaf,Num_division2) n=1; sigmar1=sigma-eval(F/dF); while abs(sigmar1-sigma)>=1.0e-6 n=n+1; sigma=sigmar1; sigmar1=sigma-eval(F/dF); end sigma=sigmar1; sigmar_2(i)=sigma; xi02(i)=xi1/2*(cos(aA*(T-As-sigma/CA))+1); Exi=EA+xi02(i)*(EM-EA); Mcofxi=1./(1+Exi*Area_SMA/Length_SMA*(1/k1+1/k2)); yu02(i)=epsilon0-(1./Mcofxi-1).*(sigmar_2(i)-sigma0)./Exi; aaa(i)=cos(aA.*(T-As-sigma/CA)); i=i+1; end T_2=linspace(Asigmas,Asigmaf,Num_division2); T_5=linspace(Asigmaf,100,Num_division1); Mcofxi=Mcofxi2; sigmar_5=Mcofxi*Theta*(T_5-Asigmaf)+sigma2; xi05=T_5-T_5; yu05=epsilon0-(1/Mcofxi-1)*(sigmar_5-sigma0)/Exi2; T_3=linspace(Asigmaf,Msigmas,Num_division2); Mcofxi=Mcofxi2; sigmar_3=sigma2+Mcofxi*Theta*(T_3-Asigmaf); xi03=T_3-T_3; yu03=epsilon0-(1/Mcofxi-1)*(sigmar_3-sigma0)/Exi3; syms T sigma xis=(1-xis3)/2*cos(pi/(sigmacrs-sigmacrf)*(sigma-sigmacrf-CM*(T-Ms)))+(1+xis3)/2; xi=xis; Exi=EA+xi*(EM-EA); omegaxi=-epsilonL*Exi; Mcofxi=1/(1+Exi*Area_SMA/Length_SMA*(1/k1+1/k2)); F=Mcofxi*(Exi*epsilon3-Exi3*epsilon3+Theta*(T-Msigmas)+omegaxi*xis-omegaxi3*xis3)+sigma3-sigma; dF=diff(F,sigma); sigma=sigma2-1; i=1; for T=linspace(Msigmas,Msigmaf,Num_division2) n=1; sigmar1=sigma-eval(F/dF); while abs(sigmar1-sigma)>=1.0e-6 n=n+1; sigma=sigmar1; sigmar1=sigma-eval(F/dF); end sigma=sigmar1; sigmar_4(i)=sigma; xi04(i)=(1-xis3)/2*cos(pi/(sigmacrs-sigmacrf)*(sigma-sigmacrf-CM*(T-Ms)))+(1+xis3)/2; Exi=EA+xi04(i)*(EM-EA); Mcofxi=1/(1+Exi*Area_SMA/Length_SMA*(1/k1+1/k2)); yu04(i)=epsilon0-(1/Mcofxi-1)*(sigmar_4(i)-sigma0)/Exi; i=i+1; end T_4=linspace(Msigmas,Msigmaf,Num_division2); figure(1) plot(T_5,sigmar_5,'-b','Linewidth',3) hold on plot(T_5,sigmar_5,'or') hold on TT=[T_1 T_2 T_3 T_4]; sigmarr=[sigmar_1 sigmar_2 sigmar_3 sigmar_4]; plot(TT,sigmarr,'-b','Linewidth',3) hold on plot(TT,sigmarr,'or') axis([0 100 80 450]) figure_FontSize=18; set(get(gca,'XLabel'),'FontSize',figure_FontSize); set(get(gca,'YLabel'),'FontSize',figure_FontSize); set(get(gca,'XLabel'),'FontName','Times New Roman'); set(get(gca,'YLabel'),'FontName','Times New Roman'); set(gca,'FontSize',figure_FontSize) set(gca,'FontName','Times New Roman') legend('Simulation','Cited from Brinson (1993)'); figure(2) plot(T_5,xi05,'-b','Linewidth',3) hold on TT=[T_1 T_2 T_3 T_4]; sigmarr=[xi01 xi02 xi03 xi04]; plot(TT,sigmarr,'-b','Linewidth',3) xlabel('T / ^oC') ylabel('\xi ') figure_FontSize=18; set(get(gca,'XLabel'),'FontSize',figure_FontSize); set(get(gca,'YLabel'),'FontSize',figure_FontSize); set(get(gca,'XLabel'),'FontName','Times New Roman'); set(get(gca,'YLabel'),'FontName','Times New Roman'); set(gca,'FontSize',figure_FontSize) set(gca,'FontName','Times New Roman') figure(3) plot(T_5,yu05,'-b','Linewidth',3) hold on TT=[T_1 T_2 T_3 T_4]; sigmarr=[yu01 yu02 yu03 yu04]; plot(TT,sigmarr,'-b','Linewidth',3) xlabel('T / ^oC') ylabel('\epsilon ') figure_FontSize=18; set(get(gca,'XLabel'),'FontSize',figure_FontSize); set(get(gca,'YLabel'),'FontSize',figure_FontSize); set(get(gca,'XLabel'),'FontName','Times New Roman'); set(get(gca,'YLabel'),'FontName','Times New Roman'); set(gca,'FontSize',figure_FontSize) set(gca,'FontName','Times New Roman') toc
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