Explicit Formulation Research Articles

On dynamic response and damage evaluation of bridge piers under far-field explosion loads

This paper aims to investigate of the dynamic response and damage mechanism of typical bridge piers under far-field explosions numerically and develop a feasible scheme for rapid damage evaluation of bridge piers. An ANSYS-AUTODYN-based explicit finite element formulation is introduced in which the dynamic input method of blast waves is developed using subroutines. The tests of drop hammer impact and far-field explosion are referenced to verify the reliability of the formulation and the mesh scale applicable to beam-column members is determined. Based on the validated formulation, the refined fluid–solid coupling models of typical single-column and double-column piers are established to explore their far-field blast responses. The effects of input parameters (i.e., the strength and angle of the blast wave,) on the pier response are analyzed. It is demonstrated that bending damage occurs in bridge piers is similar to that of cantilever beam under different strength loads, while the damage of double-column pier members under the constant displacement increases with the increase of the blast wave angle. By incorporating the crack distribution, quantitative assessing criterion and P-I diagram, a damage evaluating scheme is proposed and the damage regularities of piers under far-field blast loads are acquired. The present work can serve as a valuable reference for blast-resistant design and damage assessment of bridge piers under far-field blast loads.

Numerical Investigation of Step Size Effect on Formability of 2024-T3 Aluminum in Incremental Forming

Incremental forming (IF) is an advanced manufacturing process in which a forming tool locally deforms sheet material into a desired geometry through successive passes at incremental depths. An inherent benefit to the IF process is its formability improvement over conventional stamping; however, further enhancements will enable the forming of increasingly complex geometries. To progress the IF process towards heavy industrial use, the modeling of such processes must be further developed. Single point incremental forming (SPIF) of AA2024-T3 was modeled herein utilizing explicit formulations. The model geometry featured a nominally rectangular-shaped clamping region. A friction factor was experimentally determined and utilized within the model, which is a novel addition to this work. Formability was determined and forming limit diagrams were composed. It was found that the present model shows greater formability and underestimates plastic strain compared to experimental testing. The generation of forming limit diagrams for this material processed by IF is also a novel addition to this field.

Optimal Allocation and Sizing of Fault Current Limiters Considering Transmission Switching With an Explicit Short Circuit Current Formulation

As the power system expands with a more complex network structure, the excessive short-circuit current (SCC) has become a major obstacle to the rapid development of power system. The paper proposes a SCC-constrained planning model to determine the optimal locations and sizes of fault current limiters (FCLs) while considering transmission switching. N-1 security criterion is included to ensure that switching off lines will not jeopardize system security. One challenge is that the relationship between SCC and binary variables associated with switching states of transmission lines and activation statuses of FCLs is nonlinear and hard to obtain the exact expression. To this end, the paper begins with the equations of admittance matrix and nodal self-impedance, and derives the explicit formulation of SCC considering transmission switching and FCL activation. Based on the explicit expression of SCC, the proposed optimal allocation and sizing model of FCLs is formulated as a mixed integer linear programming (MILP) problem which could be solved by off-the-shelf commercial solver Gurobi in MATLAB. Numerical case studies on IEEE 30-bus, 118-bus and 1354-bus systems validate the effectiveness and advantages of the proposed model in reducing total costs and enhancing system security. The modeling accuracy of the explicit SCC formulation is also illustrated.

MLR-SNet: Transferable LR Schedules for Heterogeneous Tasks.

The learning rate (LR) is one of the most important hyperparameters in stochastic gradient descent (SGD) algorithm for training deep neural networks (DNN). However, current hand-designed LR schedules need to manually pre-specify a fixed form, which limits their ability to adapt to practical non-convex optimization problems due to the significant diversification of training dynamics. Meanwhile, it always needs to search proper LR schedules from scratch for new tasks, which, however, are often largely different with task variations, like data modalities, network architectures, or training data capacities. To address this learning-rate-schedule setting issue, we propose to parameterize LR schedules with an explicit mapping formulation, called MLR-SNet. The learnable parameterized structure brings more flexibility for MLR-SNet to learn a proper LR schedule to comply with the training dynamics of DNN. Image and text classification benchmark experiments substantiate the capability of our method for achieving proper LR schedules. Moreover, the explicit parameterized structure makes the meta-learned LR schedules capable of being transferable and plug-and-play, which can be easily generalized to new heterogeneous tasks. We transfer our meta-learned MLR-SNet to query tasks like different training epochs, network architectures, data modalities, dataset sizes from the training ones, and achieve comparable or even better performance compared with hand-designed LR schedules specifically designed for the query tasks. The robustness of MLR-SNet is also substantiated when the training data are biased with corrupted noise. We further prove the convergence of the SGD algorithm equipped with LR schedule produced by our MLR-SNet, with the convergence rate comparable to the best-known ones of the algorithm for solving the problem. The source code of our method is released at https://github.com/xjtushujun/MLR-SNet.

Light transport through a magneto-optical medium: simple theory revealing fruitful phenomena.

Electromagnetic wave transmission in a magneto-optical (MO) medium is a basic and old topic but has raised new interest in recent years, because MO medium plays a vital role in optical isolator, topological optics, electromagnetic field regulation, microwave engineering, and many other technological applications. Here, we describe several fascinating physical images and classical physical variables in MO medium by using a simple and rigorous electromagnetic field solution approach. We can easily obtain explicit formulations for all relevant physical quantities, such as the electromagnetic field distribution, energy flux, reflection/transmission phase, reflection/transmission coefficients, and Goos-Hänchen (GH) shift in MO medium. This theory can help to deepen and broaden our physical understanding of basic electromagnetics, optics, and electrodynamics in application to gyromagnetic and MO homogeneous medium and microstructures, and might help to disclose and develop new ways and routes to high technologies in optics and microwave.

Numerical Simulation for Hydrogen-Assisted Cracking: An Explicit Phase-Field Formulation

Hydrogen-assisted cracking is one of the most dominant failure modes in metal hydrogen-facing materials. Therefore, the hydrogen-assisted cracking mechanism has been a hot topic for a long time. To date, there is very little published research on numerical methods to describe hydrogen-assisted cracking. This paper presents a new method for the description of hydrogen embrittlement crack growth: an explicit phase-field formulation, which is based on the phase-field description of cracks, Fick's mass diffusion law, and the relationship between hydrogen content and fracture surface energy. A novel computational framework is then developed using the self-developed FEM software DYNA-WD. We numerically calculate several typical conditions in the 3-D coordinates to validate the effectiveness of the proposed computational framework. Specifically, we discuss (i) the failure of a square plate in a hydrogenous environment, (ii) the CT specimen failed with the inner hydrogen, (iii) the plate/failed with the corrosives, and (iv) the failure of the disk test. Finally, the relationship between Mises stress, the concentration of hydrogen, the thickness of the disc, and the loading rate is investigated.

A SUR version of the Bichon criterion for excursion set estimation

Many model inversion problems occur in industry. These problems consist in finding the set of parameter values such that a certain quantity of interest respects a constraint, for example remains below a threshold. In general, the quantity of interest is the output of a simulator, costly in computation time. An effective way to solve this problem is to replace the simulator by a Gaussian process regression, with an experimental design enriched sequentially by a well chosen acquisition criterion. Different inversion-adapted criteria exist such as the Bichon criterion (also known as expected feasibility function) and deviation number . There also exist a class of enrichment strategies (stepwise uncertainty reduction—SUR) which select the next point by measuring the expected uncertainty reduction induced by its selection. In this paper we propose a SUR version of the Bichon criterion. An explicit formulation of the criterion is given and test comparisons show good performances on classical test functions.

Power-product matrix: nonsingularity, sparsity and determinant

In this paper, we are interested in a special class of integer matrices, namely the power-product matrix, defined with two positive integers n and d. Each matrix element is computed by a power-product of two weak compositions of d into n parts. The power-product matrix has several interesting applications such as the power-sum representation of polynomials and the difference-of-convex-sums-of-squares decomposition of polynomials. We investigate some properties of this matrix including: nonsingularity, sparsity and determinant. Based on techniques in enumerative combinatorics, we prove that the power-product matrix is nonsingular and the number of nonzero entries can be computed exactly. This matrix shows sparse structure which is a good feature in numerical computation of its inverse required in some applications. Special attention is devoted to the computation of the determinant for n = 2 whose explicit formulation is obtained.

Grain shear stress and bed-load transport in open channel flow with emergent vegetation

The prediction of bedload transport capacity in riverbed with aquatic vegetation is a pressing need for river restoration. Laboratory experiments were conducted to investigate the weak bed-load transport rates with emergent vegetation for different energy slopes and vegetation densities. Such rate was observed to increase as the energy slope increased and the vegetation density decreased. The bed shear stress calculated by subtracting the vegetation drag from the total flow driving force was unable to predict the measured bed-load transport rate. On the other side, the estimation of the grain shear stress using the Einstein partitioning method considering the form drag provided a reasonable prediction. On the basis of these results, an explicit formulation for estimating grain shear stress was developed to predict the bed-load transport rate in a vegetated channel by considering the superimposition of forces. In addition, a simple relationship between grain shear stress and total shear stress was established by the boundary layer model. It was inferred that bed-load transport rate decreases with the increase of vegetation blocking factor while the total shear stress remains constant. Comparatively, the proposed models were more accurate than literature models, improving the understanding of the bed-load transport in a vegetated flow.

Extending Timoshenko Beam Theory for Large Deflections in Compliant Mechanisms

Abstract Compliant mechanisms (CMs) have presented its inherently advantageous properties due to the fact that CMs utilize elastic deformation of the elementary flexible members to transfer motion, force, and energy. Previously, the classic Euler–Bernoulli beam theory is the most used theory in terms of modeling large beam deflections in CMs. However, it has some assumptions that may decrease the modeling accuracy, such as ignoring the shear strain and the axial strain of cross sections. In this article, to take into account the shear and axial strains, we adopt the Timoshenko beam theory along with some modifications to consider the axial elongation. To simplify the complexity of the proposed governing boundary value problem (BVP), we transform the BVP into an explicit formulation and use weighted residual methods to numerically approximate the solution. We first focus on the single-beam deflection of a straight beam and an initially curved beam (ICB) using Euler–Bernoulli beam theory, Timoshenko beam theory, and solid mechanics to analyze the contributions of the influences of shear and axial strains in beam deflections. Then, we prove the feasibility of the proposed modeling strategy via mechanism synthesis for a bi-stable mechanism and an ICB-based parallelogram mechanism. Finally, the deduction of the mathematical model and the numerical results are provided along with brief analysis on the mechanical performances of the studied CMs.

A Curve-fit Traction Coefficient Relation of Mixed EHL Line Contact with Hydraulic Fluid and Steel Surfaces

Accurate modeling of hydraulic gear machine meshing torque loss, considering possible asperity contact, is required for better prediction of its hydromechanical efficiency. A model for predicting the mixed thermal EHL line contact traction coefficient is implemented in this study, considering experimental density and viscosity properties. Simulation results of traction coefficient are validated with experiments at two operating conditions. The defining components of the traction coefficient, the asperity load ratio and the hydrodynamic component are obtained at wide range of inputs. Finally, explicit curve-fit formulations of the asperity load ratio and the hydrodynamic component of traction coefficient are created in terms of input non-dimensional variables, which can be used for modeling the torque loss in a simple yet accurate way.

An Implicit–Explicit Second-Order BDF Numerical Scheme with Variable Steps for Gradient Flows

In this paper, we propose and analyze an efficient implicit–explicit second-order backward differentiation formulation (BDF2) scheme with variable time steps for gradient flow problems using a scalar auxiliary variable (SAV) approach. Comparing with the traditional second-order SAV approach (Shen et al. in J Comput Phys 353:407–416, 2018), we only use a first-order method to approximate the auxiliary variable. This treatment does not affect the second-order accuracy of the unknown function $$\phi $$ , and is essentially important for deriving the unconditional energy stability of the proposed BDF2 scheme with variable time steps. We prove the unconditional energy stability of the scheme for a modified discrete energy with the adjacent time step ratio $$\gamma _{n+1}:=\tau _{n+1}/\tau _{n}\le 4.8645$$ . The uniform $$H^{2}$$ bound for the numerical solution is derived under a mild regularity restriction on the initial condition, that is $$\phi ({\varvec{x}},0)\in H^{2}$$ . Based on this uniform bound of the numerical solution, a rigorous error estimate of the proposed scheme is carried out on the nonuniform temporal mesh. Finally, serval numerical tests are provided to validate the theoretical claims. With the application of an adaptive time-stepping strategy, the efficiency of our proposed scheme can be clearly observed in the coarsening dynamics simulation.

ИССЛЕДОВАНИЕ УДАРНОГО ОТКЛИКА СОТОВОЙ КОНСТРУКЦИИ С ТОНКИМИ ОБШИВКАМИ ИЗ РАЗЛИЧНЫХ МАТЕРИАЛОВ

The use of honeycomb sandwich panels in the national economy has become widespread recently. Their advantages are the relative lightness with good strength capabilities. The article presents a calculation of the impact response between a honeycomb sandwich panel and an absolutely rigid spherical body. The value of internal and kinetic energy, as well as equivalent stress in a sandwich panel, is determined. The influence of materials of thin skins of sandwich panels on above values is analyzed. The problem is solved with computer simulation of the dynamic process in an explicit formulation. The work results are relevant in the design of structures that combine optimal strength and weight characteristics.

Physics-Constrained Robustness Evaluation of Intelligent Security Assessment for Power Systems

Machine learning (ML) algorithms have been widely developed to enable real-time security assessment for large-scale electricity grids. However, it also has been extensively recognized that the ML models are vulnerable to adversarial examples, which are slightly perturbed instances that can mislead the classifications but cannot be distinguished by human eyes. Considering the adversarial examples against the ML-based security assessment, they must not only cause misclassification but also follow the power balance and transfer limits and bypass the bad data detection. To this end, this paper proposes a novel concept named physics-constrained robustness that aims to computing a lower-bound of adversarial perturbations, evaluating the vulnerability of the ML-based intelligent security assessment (ISA) for power systems. A general optimization problem is formulated to compute the physics-constrained robustness of ISA with the mislabeling, power balance, power limitation, and invisible constraints. The analytical results and comparing relationship of ISA’s robustness with different constraints are provided. By using the static security assessment as an example, we provide explicit formulations to evaluate the physics-constrained robustness of. Finally, extensive experiments are conducted to evaluate the physics-constrained robustness of ISA in static and dynamic cases with the real-world load profiles from New York State and provide suggestions to select the ML models and parameters.

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures

Porous material structures have been widely used in civil engineering, mechanical engineering, aerospace engineering and other fields due to their high specific strength and specific stiffness. The stochastic response analysis of porous material structures under random excitations deserves more attention. The multiscale differential governing equations of porous material structures are derived based on the multiscale asymptotic homogenization method (AHM), and the macroscale and microscale explicit time-domain expressions of structural responses are further established. On this basis, the statistical moments of dynamic responses of porous material structures under non-stationary random excitations can be achieved with the explicit time-domain method (ETDM). The purposed method combines the advantages of AHM for high-efficient explicit formulation of macroscale and microscale dynamic responses of porous material structures and the advantages of ETDM for fast analysis of non-stationary random vibration problems. A numerical example is presented to validate the computational accuracy and efficiency of the present approach for non-stationary random vibration analysis of porous material structures.

Modeling hydraulic fracture fluid efficiency in tight gas reservoirs using non-linear regression and a back-propagation neural network

ABSTRACT This study introduces a back-propagation (BP) neural network model and a regression model for estimating the fracture fluid efficiency based on a data set consisting of 1261 staged and ramped simulation runs of tight gas reservoirs subjected to hydraulic fracturing treatment. Data were generated using a 3-D commercial simulator which is a versatile software portfolio that models many well configurations, proppant placement, and fracture geometries. The BP network inputs consist of shear rate/fracture conductivity ratio, the injection rate, reservoir permeability, formation closure stress, reservoir thickness, effective viscosity, and fracture height. The neural network model was able to generate satisfactory estimates of the fracture fluid efficiency for the training dataset, and for the blind testing data. An average error of approximately 2.5% was obtained for the training set, and an average error of 3% was obtained for the testing set. An empirical non-linear regression model has been constructed based on dimensionless groups derived by applying dimensional analysis to a set of variables consisting of the maximum fracture width, fracture length, fracture height, effective viscosity, shear rate/fracture conductivity ratio, reservoir thickness, injection rate, reservoir permeability, and formation closure stress. The average error for estimating the fluid efficiency using the non-linear regression empirical model was approximately 6.17%. Since the non-linear regression model has an explicit formulation, it is easier to apply than the neural network model. The empirical regression model estimates of the fluid efficiency appeared to be unbiased and were more precise than those estimates obtained using either the KGD or the PKN 2-D models. The introduced BP model and the non-linear regression model offer fast and inexpensive alternatives to the application of three-dimensional simulators for estimating the fluid efficiency.

An efficient surrogate model-based method for deep-towed seismic system optimization

The towing speed, cable length, towing depth, and hitch position should be optimized to improve the operational safety and efficiency of a deep-towed seismic system. However, the optimization is ineffective due to system nonlinearity and large-scale calculations. Therefore, a surrogate model-based method is proposed to simplify a deep-towed system and promote system optimization. The relationships among the towing speed, viscous drag and pitch angle of the towed vehicle are expressed using a surrogate model generated by using the artificial neural network method. Input variables of the surrogate model are related to the optimization variables through proper design variable selection, which generates an efficient explicit formulation. Additionally, a quasi-static iteration is established to speed up calculating the cable shape of the towing cable, and analytical models simplify the calculations of drag forces acting on the drogue and seismic array. Finally, the best design, such as the towing speed, cable length and hitch position, are obtained with limited cable tension and towing depth in a case study. This research provides an effective method for deep-towed seismic system optimization.

Optimality equivalence and computational advantages of free-floating base dynamics compared to full-body dynamics

Several transcription methods exist for predictive simulations of free-floating base motions like athlete performing twisting somersaults. Following a brief overview of the literature, we proposed two original direct multiple shooting optimal control problems: (1) with a reduced set of equations motion (free-floating base dynamics) and generalized accelerations as controls; and (2) with the dynamics enforced implicitly through algebraic constraints and generalized jerks as controls. To assess their performance (computational time, dynamic consistency, cost), we compared full-body vs free-floating base dynamics and explicit vs implicit formulations of an optimal control problem of a double straight somersault with three twists. We found that free-floating dynamics is relevant when bounds on joint torques are not required since it hastens the convergence up to 10 times and the optimal solutions are similar. Implicit dynamics also speeds up optimization compared to the explicit formulation, but dynamic consistency may be affected. Using joint jerks instead of accelerations as controls mitigates this limitation, especially when the mesh grid densifies.

The Quasi-Keplerian Motion of the Charged Test Particle in Reissner-Nordström Spacetime under the Wagoner-Will-Epstein-Haugan Representation

We present the post-Newtonian solution for the quasi-Keplerian motion of a charged test particle in the field of Reissner-Nordström black hole under the Wagoner-Will-Epstein-Haugan representation. The explicit formulations for the charge effects on perihelion precession and the orbital period are achieved, which may be useful not only in the comparisons with astronomical observations but also in calculating the waveform of the gravitational wave from this kind of system.

ANALYSIS OF MESOSTRUCTURE AND FRACTURE KINETICS OF ELEMENTS OF LATTICE COMPOSITE STRUCTURES UNDER TRANSVERSAL COMPRESSION USING STOCHASTIC FEA MICROMECHANICS

The paper analyses the mesostructure of the structural elements of lattice aircraft shells – ribs consisting of alternating layers of equal thickness and made from unidi-rectional CFRP and pure matrix material. In experimental studies, the elastic characteristics of unidirectional CFRP were obtained under three-point bending and transversal compression. As a result, the longitudinal modulus of elasticity of the layered composite turned out to be 101 GPa, and the shear modulus was 2.95 GPa. Numerical modeling of the meso- and micromechanics of the interaction of the noticed layers under transversal compression has been performed up to failure. The ANSYS FEA software (explicit and implicit formulations) was used. The regular and stochastic stacking of fibres in the cross section under compression is considered. The fiber diameters in the composite element were measured on thin sections using a Zeiss Axio Observer D1m digital microscope and were equal to 5.1 ± 0.8 µm. Layers with a fiber volume fraction of about 60 % alternate with layers of pure epoxy. It is proposed to use only the first principal stress in the matrix as a micromechanical criterion for failure under com-pression and tension. At the first stage of calculations, the problem of transversal compression of a cell with a regular laying of fibres was solved (the error in the value of the transversal modulus of elasticity was less than 2 %). At the second stage, an assessment was made of the strength and accumulation of microdamages under compression in a model of a layered structure with stochastic fibre stacking. The analysis of stress-strain state of a layered mesostructure under compression made it possible to explain the reason that the rib has a trans-verse strength twice lower than that of a homogeneous CFRP. The calculated values of the ultimate strength in transversal compression of a layered rib are in good agreement with the experimental ones.