THE INFLUENCE OF THE BALANCE FACTOR IN THE DISTANCE-MINIMIZING DATA-DRIVEN COMPUTATIONAL METHOD

Data-driven computational methods transform the solution of the simultaneous equations of equilibrium, geometric, and material constitutive laws into an optimization problem. The optimization goal is to search for the best fitted statically-admissible stress field, kinematically-admissible strain field, and stress-strain data assignment. Based on the linear elastic theory, the influence of the magnitude m and the parallel deviation r of the balance factor relative to the material constants on the convergence rate and performance are discussed. The results show that the admissible stress and strain converge linearly at rates of 1/(1+m²) and m²/(1+m²), respectively, in the relaxation problem. Meanwhile, the convergence rates for both the admissible stress and strain decrease with increased r. The assigned data are limited by integral constraints in the original optimization problem, and the low change rate between adjacent iteration steps leads to premature convergence. The stress-strain data approximate the reference solution along a straight path in phase space when r is equal to zero. The gradual linear convergence rate reaches the minimum when m is set to 1. When r is not zero, the iterative path of the data no longer remains a straight line. For the components with a smaller convergence rate, the deviation from the reference solution increases when the iteration stops. The density of the data points near the exact solution provides guaranteed accuracy for the algorithm, thereby reducing the sensitivity of the computational result to the balance factor.