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In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.
This paper presents several aspects of characterization of welding heat source parameters in Goldak’s double ellipsoidal model using Sysweld simulation of welding of two overlapping beads on a substrate steel plate. The overlap percentages ranged from 40% to 80% in increments of 10%. The new material properties of the fused metal were characterized using Weldware and their continuous cooling transformation curves. The convective and radiative heat transfer coefficients as well as the cooling time t8/5 were estimated using numerical formulations from relevant standards. The effects of the simulation geometry and mesh discretization were evaluated in terms of the factor F provided in Sysweld. Eventually, the parameters of Goldak’s double ellipsoidal heat source model were determined for the welding simulation of overlapping beads on the plate and the simulated bead geometry, extent of the molten pool and the HAZ were compared with the macrographs of cross-sections of the experimental weldments. The results showed excellent matching, thus verifying this methodology for determination of welding heat source parameters.
This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.