A hybrid interval uncertainty algorithm for structural analysis
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A variety of methods have been proposed for analyzing structures with interval parameters, each with distinct strengths and limitations depending on the problem characteristics. In the context of structural analysis, intrinsic methods typically involve directly solving the governing interval equations using algorithms that preserve the interval nature of the parameters, without relying on transformations or approximations. These methods are generally efficient and provide guaranteed solution bounds for response quantities. Still, a common challenge arises when the parameterization of a few parameters is nonlinear, such as when the loading direction is unknown but bounded. By contrast, extrinsic methods reformulate the interval problem as an optimization problem, where external optimization techniques are applied to identify the extreme responses within the prescribed interval ranges. While extrinsic approaches often provide an interval solution within the interval constraints, they are computationally demanding and do not provide a guaranteed bound on a solution. This paper explores a hybrid interval approach that integrates both intrinsic and extrinsic strategies to solve systems of linear interval equations more effectively. The hybrid framework applies intrinsic methods where computational efficiency is critical and employs extrinsic optimization where the interval parameterization is nonlinear, thereby exploiting the complementary advantages of each method. Example calculations are presented to compare the performance of the hybrid approach against conventional extrinsic optimization-based methods. The results demonstrate that hybrid methods achieve more efficient computations and deliver solutions closer to the correct bounds than extrinsic calculations alone, making them a practical and robust tool for interval-based structural analysis.
