General weight functions only containning three coefficients for eccentric through cracks in a 3-D rectangular plate subjected to complex nonlinear loading were proposed. Three sets of reference stress intensity factors of 3-D rectangular cracked plate were obtained by the finite element method

and combining with binary Lagrange interpolation method

the three coefficients of each general weight function were also obtained. Self-consistency of general weight functions was verified and general weight functions were also validation when the crack surface was loaded by simple third-order

fifth-order

seventh-order

complex power law stress distributions and the residual stress distribution were conducted. Results showed that

the self-consistency error of general weight functions was smaller than 0.9%

when the crack surface was loaded by the complex power law stress distribution

error of the weight function method was smaller than 4.5%

when the crack surface was loaded by the residual stress distribution

error of the weight function method was smaller than 8.5%. This indicates that the proposed general weight functions has high computing accuracy

which could meet the challenge of calculating stress intensity factors of eccentric through cracks subjected to arbitrary complex nonlinear loading efficiently and correctly in engineering.