@Preben Alsholm Sir.... actually...the equation is like this......this is the governing equation for damage accumulation model of composite under fatigue loading...i consider with sinusodial loading case
  i have some derivation...dD/dt = some function and....finally we get   

D(t) = 1-(1-C(1+k) integral 0 to N (sigma_a * sin(omega*t))^k dt........

if i can get closed form solution..i can plot damage accumlation vs number of load cylce ...
and and loading parttern is a choice .. ....i can get closed form with different type of loading history..for eaxmple ( constant trapezodial pattern)..but sinusoidal loading are actually easy and cheap to set up  experiment and ...the problem is i don't get closed form solution for integral term.

@aroche it's still show integral..not solution...here is the problemintegral.mwintegral.mw

@Preben Alsholm yes.Sir..but please check this equation.....
d(n)=int( (sin(omega*t))^k,t=0..N
i have eqautino like this...and maple didn't solve that equation by default...is that maple crack..or this eqaution doesn't converge....is there any other way..to solve this eqaution

@acer yes.Sir..but please check this equation.....
d(n)=int( (sin(omega*t))^k,t=0..N
i have eqautino like this...and maple didn't solve that equation by default...is that maple crack..or this eqaution doesn't converge....is there any other way..to solve this eqaution

@Preben Alsholm thank you sir...but in my problem k is parameter have to decide..from experimental data with curve fitting..is there any way..to solve symbolically with k prescence...N is loading cycle ...and n is cycle to failure ..this is cyclic loading problem....
the problem is k is material constant.....can you help ..without getting rid of k....MaplePrimes24-04-04_int_bug.mw

i go to the axes properties. and used tick marks..it doesn't change..can you please check my plot here is my m.file

45.mw

@mmcdara 
thank you Sir...i got it...i need intital guess values from some paper and sovle it form what your guided model...and it help me a lot  ...here is mine...it is pretty valid i think and need to verify that from my supervisor
By the way...this is the prediction of stress-strain curve of unidrectional composite laminate under strain rate loading....yours are quite helpful......than you very much...Sir..wish you the best

@mmcdara thank you sir...i'm a student  and...this is for my thesis..sir..actually i don't have ...enough data for intital value..here is the error is reduced..but still too high....that you very much..sir..yours ..is absolutely helpful
9terms.mw
can you check please...look like need to determine.constraints..more effectvely?
that you very much sir

@mmcdara 
thank you sir....e  is exponential..and G values are prony coefficient and tau values are relaxation times...
should i put e and nu(poission ratio) to parameters..poission ratio is given and e is exp...
can you give me how to put intial point to maple worksheet...i already tried intital points also...but still some error for this.
here is my maple worksheeet..sir....i really appritiated that.prony.mw

@sand15 
thank you Sir
here is my new worksheet..here is error
Error, (in Optimization:-Minimize) objective function must be an algebraic expression or procedure
prony.mw

@acer sir i change the variable values and equations a litle bit and i have the error like this..i want to solve for t= 0 to 600 s ..can you check this please

Download time-dependent_aerodynamic_pressure.mw

@rlopez  sir. the plot is like this i want t is bottom but its in the top and it is too large how can i fix it..? with respect

@mmcdara 
 thank u sir ..but i don't think i want that animation...may be i'm wrong with my equations....please check this..
 

i want to plot (epsilon,time) for all value of time....in this equation
plot_matrix_over_time.mw

@tomleslie thank u sir ..but i don't think i want that animation...may be i'm wrong with my equations....please check this..
 

i want to plot (epsilon,time) for all value of time....in this equation
plot_matrix_over_time.mw

@acer   thank u sir ..but i don't think i want that animation...may be i'm wrong with my equations....please check this..
 

i want to plot (epsilon,time) for all value of time....in this equation
plot_matrix_over_time.mw