Abstract
A numerical approach is developed to apply to numerical calculations for a CFRP strengthened steel member, in which multiple precistion arithmetic is used for removing numerical instability inherent in numerical schemes constructed under a fixed precision arithmetic method. First, by supposing a steel member with a bonded CFRP plate under tensile loading, a system of differential equations describing spatial variation of axial force and shear force of CFRP plate. A numerically solving framework is further constructed based upon a transfer matrix method, where a boundary value problem is equivalently replaced by an initial value problem. It is shown that the numerical instability appearing in a numerical scheme under the fixed precision arithmetic method defined by IEEE 754 can be effectively removed by the use of the multiple precision arithmetic method. Further it is clarified that (i) a proposed approach can be applied to a case of bonding CFRP with tapers at their ends, (ii) obtained solutions show qualitatively good agreement with finite element analysis results and (iii) a proposed approach can give accurate estimations for stress concentration closely near the end of CFRP plate.
