Learning the Solution Operator Family in Elastic Mechanics for Response Prediction Under Various Load Scenarios

Analyzing the responses of solid materials under diverse loading scenarios with different types and forms is a fundamental engineering necessity. However, a load-adaptable machine learning model that can predict such responses still needs to be explored. This study formulates the load-adaptable response prediction problem as a solution operator family regression task and develops a Load-Adaptable Physics-Informed DeepONet (LA-PIDON) to learn the solution operator family of mechanics. The proposed method utilizes the product space as the input space, composed of function spaces for force boundaries, displacement boundaries, material properties, and other mechanical factors. Distinct branch networks are established for each mechanical factor and distinct trunk networks for each corresponding response. The solution family learning task is accomplished by using shared branch networks across multiple trunk networks. The load adaptability for both concentrated and distributed forces is achieved through the integration of Gaussian Random Fields(GRFs) and Fourier polynomials to generate function spaces for the force boundary; the load adaptability for force and imposed displacement excitation is achieved by incorporating the product space of force and displacement boundaries into the input space. The numerical cases of (1) elastic plates subjected to benchmark force and imposed displacement excitations, (2) benchmark beams under pure and tensile bending, and (3) 3D elastic cubes undergoing axial tension demonstrate the method's adaptability to various load scenarios and its capacity to handle complex stress states. The proposed method has potential applications in fields that require numerous simulations for diverse load scenarios, such as reliability analysis and digital twins.