Closed-form integration of Slip ODE for anchored FRP–concrete joint with exponential Bond–Slip law

Questions
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1

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Hi all. This expression arises from equilibrium and compatibility in the
anchored region, where the bond–slip law includes an exponential
cohesive term and a nonzero residual shear stress

I would like to know:

  1. Whether this integral admits a closed-form analytical solution (exact or implicit).

  2. Whether asymptotic or approximate closed-form solutions are only options.

Any guidance or references would be appreciated.

2

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3

Practical conclusion:

Generic case: No closed-form analytic antiderivative in elementary or standard special functions.

Only in special parameter regimes (t=0 ,B=0, or fine-tuned constants) does a closed form exist.

Otherwise: One must use numerical quadrature, or asymptotic / perturbative approximations.

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4

Thanks a lot for the effort. Yes, for t=0, there exists a closed form antiderivative. At last, I am going ahead with the numerical solution as any other solution will not do the job for me. Thanks again!