Inaccurate Boundary Conditions Research Articles

Multi-scale analysis method for composite-metal hybrid truss nodes using the MPC-submodel approach

Large-scale composite material-metal composite structures subjected to multi-axial loading conditions experience stress concentration and damage due to the dissimilar mechanical properties of the materials. A multi-scale refined modeling analysis is essential for accurately investigating these hybrid truss nodes. However, the existing multi-scale analysis methods face certain challenges, including modeling difficulties, reduced computational efficiency, convergence issues, and inaccurate boundary conditions. In this study, we first proposed an MPC-submodel approach based on the submodeling method and the multi-point constraint (MPC) technique to address these challenges in multi-scale computations of large-scale structures. Subsequently, we conducted experimental tests on composite-metal hybrid trusses and performed finite element simulations on key nodes using the proposed method, validating its accuracy. Finally, we applied the proposed method to investigate the key nodes within a 200-m long-span composite-metal composite truss bridge. By comparing the results with those from finite element simulations using the multi-point constraint method, we effectively demonstrated the advantages of the proposed method. The results indicated that our approach accurately modeled boundary conditions, significantly reduced computational time, and improved efficiency while maintaining computational accuracy.

An effective LRTC model integrated with total α ‐order variation and boundary adjustment for multichannel visual data inpainting

Restoring damaged multichannel visual data with high loss ratio is quite a challenging task. To address this problem, an effective LRTC (low-rank tensor completion) model integrated with total α-order variation (TVα) in the fractional bounded variation space BVα is proposed to perform superior fractional-in-space regularization. Based on using LR constraint to restore global patterns, TVα regularization is integrated to exploit nonlocally-correlated information on each channel to infer the lost data and simultaneously effectively deal with complex details due to the powerful fractional calculus. Then, a nonlocal fractional regularization strategy for multi-dimensional data and an effective numerical optimization method are creatively designed to solve this problem. Two novel fractional derivative matrix approximations are derived and applied to the first two unfolding modes of the tensor respectively to conveniently solve the fractional regularization subproblem by using an element-wise shrinkage-thresholding operation. In addition, boundary extension and adjustment strategy are designed for the unfolded matrices to alleviate the influence of inaccurate boundary conditions in fractional derivative computations. Experiments are conducted to illustrate its performance and efficiency for YUV video, RGB and HSI restoration, especially its ability to effectively recover complex structures and the details of multi-component visual data with relatively high missing rate.

Review and analysis of heat source models for additive manufacturing

As additive manufacturing (AM) becomes a viable manufacturing solution, demand for an accurate thermo-structural model of the process increases. Iteratively correcting discrepancies between the CAD model and additively manufactured product through trial and error can be an expensive and time-consuming process, taking up to several hours to build and costing up to tens of thousands of dollars Lindgren et al. (Addit Manuf 12:144–158, 2016). A numerical model reduces manufacturing cost and time considerably by predicting discrepancies that will arise due to the complex thermal history induced by the AM process, thus reducing the need for iterative manufacturing. An important part of any additive manufacturing model is the heat source model. The heat source model is a mathematical function which represents how much of a heat source’s power actually goes into heating the powdered metal and how this heat is distributed across the heat-affected zone (HAZ). This paper provides a review and analysis of heat source models in the AM literature to date in order to alleviate some of the confusion and provide emerging researchers in the field with perspective on the issue. Both two-dimensional surface models and three dimensional volumetric models are explored. Next, an analysis of the models was performed and presented in an effort to validate their physical accuracy and mathematical usability. This analysis consisted of checking for sensible boundary conditions and ensuring that energy conservation is upheld. In surface models, the TEM00 model is a classic representation of the Gaussian power distribution of most heat sources used in AM. Researchers interested in simply modeling the heat distribution, without accounting for any other phenomena that intervene in the heat transfer process (such as molten pool dynamics) will find the TEM00 model suitable. The literature also shows cases where the TEM00 model has been modified to have a sharper radial gradient, and these modifications can be suitable for high-powered heat sources. For volumetric models, Goldak’s ellipsoidal model (Metall Trans B 15(2)299–305, 1984) remains a straightforward and accurate model that is physically sound and applicable to a variety of cases. The Gaussian cone model presented by Rogeon et al. [48] also performs well, meeting all the required physical and mathematical restrictions. This model’s linearly decaying penetration is better suited for high-energy applications. The non-Gaussian cone proposed by Tsirkas et al. (J Mater Process Technol 134(1):59–69, 2003) imposes inaccurate boundary conditions and violates the first law of thermodynamics, and is thus deemed an inadequate model. Other novel models have been introduced in recent years, most notably the line model and the elongated ellipsoidal model presented by Irwin and Michaleris (J Manuf Sci Eng 138(11):111004, 2016). Both of these models are based on Goldak’s ellipsoidal model and attempt to maintain the accuracy of that model while allowing for fewer time steps and requiring less computational resources. These models appear to function well and can be used effectively in some applications, but could benefit from further study and validation. Care must be taken to ensure that the parameters used with these models do not result in averaging errors or a discontinuous thermal field. These tools must be used carefully with a thorough understanding of the underlying mathematics.

Parametric model updating with frequency and MAC combined objective function of port crane structure based on operational modal analysis

Abstract In FE modeling of port crane structures, errors may be caused due to the simplification of complicated components, unclear physical properties, local approximation and inaccurate boundary conditions. So it is very important to update the FE model accuracy according to the experiment model and results. However there are two major problems when solving the model updating of port crane structure, the one is the difficulty of collecting the structure modal parameters with traditional modal experiment method because of the large scale of port crane structure, the other is mismatching problem while updating processing due to most of the model updating method currently constructing the objective function only by frequency. In this paper, an operational modal analysis is adopted to estimate the modal parameters of port crane structure based on the operational condition. A parametric model updating methodology of finite element (FE) model is proposed to solve port crane structure model updating: a series of design parameters of the FE model of port crane structure are selected as the main factors based on the sensitivity analysis, the objective function is built by considering the frequency correlation and the modal assurance criterion (MAC) together, and finally a zero-order/first-order combination algorithm is utilized to get the final accurate FE model of port crane structure. Research results showed that methodology proposed in this paper has satisfied updating accuracy for port crane structure, which verifies that the proposed method is suitable for model updating problem of this kind of structure.

Highly adaptive liquid simulations on tetrahedral meshes

We introduce a new method for efficiently simulating liquid with extreme amounts of spatial adaptivity. Our method combines several key components to drastically speed up the simulation of large-scale fluid phenomena: We leverage an alternative Eulerian tetrahedral mesh discretization to significantly reduce the complexity of the pressure solve while increasing the robustness with respect to element quality and removing the possibility of locking. Next, we enable subtle free-surface phenomena by deriving novel second-order boundary conditions consistent with our discretization. We couple this discretization with a spatially adaptive Fluid-Implicit Particle (FLIP) method, enabling efficient, robust, minimally-dissipative simulations that can undergo sharp changes in spatial resolution while minimizing artifacts. Along the way, we provide a new method for generating a smooth and detailed surface from a set of particles with variable sizes. Finally, we explore several new sizing functions for determining spatially adaptive simulation resolutions, and we show how to couple them to our simulator. We combine each of these elements to produce a simulation algorithm that is capable of creating animations at high maximum resolutions while avoiding common pitfalls like inaccurate boundary conditions and inefficient computation.

Automatic Assessment of Uncertainties in the Case of Urban Flood Modeling

Urban flood modeling has long been attracting attention from hydraulic modelers. Due to the complicated floodplain topography, inaccurate boundary conditions, etc, uncertainties will arise from urban flood simulations and should be addressed properly. The present study deals with a novel contribution to the field of urban flood modeling with the aim to quantify uncertainties by examining the response of a finite volume two-dimensional hydraulic model, RUBAR20, used for simulating urban flooding at a crossroad. Two methods have been launched to assess uncertainties and the confident range of the solutions. The first method is the well-known Divided Differences (DD) approximation. The second method is a recently developed technique, based on the computation of derivatives using Automatic Differentiation techniques (AD). For the second method, Tapenade software has been used to calculate derivatives of the water depth with respect to the boundary conditions and roughness coefficients. Benchmark tests were carried out against well-known flows using a high quality and high spatial resolution data set collected from laboratory open channels. Both methods provided good solutions for a reasonable set of parameters. Moreover, the AD adjoint model is found to be useful in the case of large number of input parameters.

Unipolar ion sheath

In technical applications, the ion sheath in front of a highly negative wall is frequently described by the well known Child–Langmuir law. Due to inaccurate boundary conditions, however, this yields only a rather poor approximation. The collisionless Child–Langmuir law can be substantially improved by accounting for universal initial conditions following from the Bohm criterion. By a simple analytical ansatz the resulting unipolar ion sheath law is generalized to account for (charge exchange) ion collisions in the sheath.

Two Kinds of Predictability in the Lorenz System

The Lorenz system is used to discuss two kinds of predictability: the model sensitivity to inaccurate initial conditions (first kind) and to inaccurate boundary conditions (second kind). The first kind of predictability has been investigated for a long time, but not the second kind. It was found that the Lorenz system has a capability to detect both kinds of predictability since the boundary condition is represented by a model parameter, r. Two sensitivity runs are designed by perturbing the initial condition and the model parameter r by the same small relative error (1024), which is equivalent to 10% of the instrumentational accuracy for surface temperature measurement. Comparison of model output between the control run and the sensitivity runs shows that the model error growth and the growing period are comparable between the two kinds of predictability. This indicates the importance of preparing accurate boundary conditions in numerical prediction.

Integration of a semi‐implicit model with time‐dependent boundary conditions

Abstract A semi‐implicit barotropic primitive equations model is integrated over a limited area with time dependent boundary conditions using the standard mesh and a finer mesh. Following a theorem by Charney, a minimum number of variables are specified as boundary conditions for the limited area integrations in order to avoid mathematical over‐specification. The comparison of coarse mesh limited area forecasts with the corresponding forecasts made over a much larger domain demonstrates that the essential features, namely the Rossby type perturbations, are handled almost perfectly. The fine mesh forecasts over the same limited area are also very good. Finally, the effect of specifying inaccurate boundary conditions, in the form of twelve‐hour forecasts, is briefly illustrated.