The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.

This paper presented a two-dimensional, well-balanced hydrodynamic and sediment transport model based on the solutions of variable density shallow water equations (VDSWEs) for sediment-laden flows, and the Exner equation for bed changes. Those equations are solved in a coupled way by the first-order Godunov-type finite volume method. The Harten-Lax-van Leer-Contact (HLLC) Riemann solver is extended to find the local Riemann fluxes in order to maintain the exact balance between the momentum term and the bed slope term. The advantage of a well-balanced scheme over an unbalanced scheme is demonstrated by the synthetic standing contact-discontinuity test case. Then, the model is employed to simulate two laboratory experiments. At last, a field case, the 1996 Lake Ha! Ha! flood event (Canada), is simulated. Results of cross sectional geometries and profiles of longitudinal thalweg agree well with measurements. The accuracy and simplicity of the numerical model, together with the robust implementation, make the model a good candidate for practical engineering applications.

Long-span steel structure trusses are widely used in factory buildings, but with the growth of service time and the increase of dynamic load fatigue, a considerable part of the long-span truss with dynamic load appears serious transverse cracks at the bottom of the middle span and oblique deformation of the abdomen in the operation process. The U-shaped cracks at the bottom and belly, as well as the mid-span down deflection of the main truss, reduced the functional function of the factory building truss structure, and had to limit the original crane load, which affected the normal safety and durability of the structure. Therefore, the application principle of the variable axial force cable system in the long-span factory building truss structure and 3D3S software modeling [1] were used. Analyzing and studying the reinforcement method of large-span powerhouse truss can provide practical experience for subsequent similar projects. In view of the above phenomenon, the large-span powerhouse trusses of Hongcheng Powerhouse 1 and No.2 located in Tonglu, Zhejiang Province are used as the research object, and the variable axial force cable method is proposed to strengthen and lift the load. Considering the span of large-span powerhouse truss, the cable system with 22m controlling force of 400kN is proposed to be selected for powerhouse 1, and the cable system with variable axial force of 24m is proposed to be selected for Powerhouse 2. The force model of large-span truss is established by using the finite element method commonly used to analyze the force of truss. Under two working conditions, The influence of reinforcement effect is analyzed and compared from three aspects: stiffness, bearing capacity and stability. And the phenomenon of uneven stress distribution is analyzed. The stress distribution characteristics of each node are understood by simulating the most disadvantageous node plates with the greatest internal force before and after reinforcement.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.

Recently, there has been, on the one hand, an increase in the complexity of digital device designs and, on the other hand, an increase in the requirements for the development time and the reliability of the designs. One of the directions of solving this problem is developing new techniques for designing digital devices.This paper proposes a new technique for designing digital devices based on finite state machines with datapath (FSMD), when the functioning of the device is described in the form of an algorithm state machine with datapath (ASMD) charts. The new technique is called ASMD-FSMD. Different digital device design techniques are compared to each other using design examples of a synchronous multiplier on field programmable gate array (FPGA). The efficiency of the ASMD-FSMD technique compared to the traditional approach in terms of area and performance was investigated. The ASMD-FSMD technique, compared to the traditional one, reduces the area from 28.6% to 39.7% and increases the speed for some designs to 17.6%. In addition, using the ASMD-FSMD technique significantly reduces design time and increases design reliability. In conclusion, recommendations for using the ASMD-FSMD technique are made.

H-adaptivity is an effective tool to introduce local mesh refinement in FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures such as ship hulls. In engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called ‘h-adaptive element splitting’ (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that consist of structured coarse meshes. By employing the mesh refinement introduced in this paper, very small cracks are well represented in large structures.

Advanced Finite Element (FE) modeling and simulations were performed on vehicular crashes into a Three-bar Metal Bridge Rail (TMBR). The FE models of a sedan, a pickup truck, and a TMBR section were adopted in the crash simulations subject to Manual for Assessing Safety Hardware (MASH) Test Level 2 (TL-2) and Test Level 3 (TL-3) requirements. The test vehicle models were first validated using full-scale physical crash tests conducted on a two-bar metal bridge using a sedan and a pickup truck with similar overall physical properties and sizes to their respective vehicles used in the simulations. The validated vehicular models were then used to evaluate the crash performance of the TMBR using MASH Evaluation Criteria for structural adequacy, occupant risk, and post-impact trajectory. The TMBR met all MASH TL-2 requirements but failed to meet the MASH TL-3 Criteria H and N requirements when impacted by the sedan. The TMBR was also evaluated under in-service conditions (behind a 1.52-m wide sidewalk) and impacted by the sedan under MASH TL-3 conditions. The simulation results showed that the TMBR behind a sidewalk met all safety requirements except for the occupant impact velocity in the longitudinal direction, which exceeded the MASH limit by 3.93%.

The safety of lithium-ion batteries is critical to the safety of battery electric vehicles (BEVs). The purpose of this work is to develop a method to predict battery thermal runaway in full electric vehicle crash simulation. The thermal-electrical-mechanical coupled finite element analysis is used to model an individual lithium-ion battery cell, a battery module, a battery pack, and a battery electric vehicle with 24 battery modules in a live circuit connection. The lithium-ion battery is modeled using a representative approach, with each battery internal component individually modeled to represent its geometric shape and realistic thermal, mechanical, and electrical properties. A resistance heating solver and Randles circuit model built with generalized voltage source are used to simulate the battery electrical behavior. The thermal simulation of the battery accounts for the heat capacity and thermal conductivity of various cell component materials, as well as heat conduction, radiation, and convection at their interfaces. The mechanical property of battery cell and battery module models is validated using spherical punch tests. The electrical property of the battery cell and battery module models is verified against CircuitLab simulation in an external short circuit test. The simulation result of battery module’s internal resistance agrees with the experimental data and the literature value. The multi-physics coupling phenomenon is demonstrated with a cylindrical compression simulation on the battery module. The multi-physics BEV model with 24 live battery modules is used to simulate the external short-circuit test and the side pole impact test. The simulations run time is less than 24 hours. The results demonstrated the feasibility of using representative battery model and multi-physics analysis to predict battery thermal runaway in full electric vehicle crash analysis.

The load cell is an indispensable component of many engineering machinery and industrial automation for measuring and sensing force and torque. This paper describes the design and analysis of the strain gauge load cell, from the conceptional design stage to shape optimization (based on the finite element method (FEM) technique) and calibration, providing ample load capacity with low-cost material (aluminum 6061) and highly accurate force measurement. The amplifier circuit of the half Wheatstone bridge configuration with two strain gauges has been implemented experimentally with an actual load cell prototype. The calibration test was conducted to evaluate the load cell characteristics and derive the governing equation for sensing the unknown load depending on the measured output voltage. The measured sensitivity of the load cell is approximately 15 mV/N and 446.8 µV/V at a maximum applied load of 30 kg. The findings are supported by FEM results and experiments with an acceptable percentage of errors, which revealed an overall error of 6% in the worst situation. Therefore, the proposed load cell meets the design considerations for axial force measurement for the laboratory test bench, which has a light weight of 20 g and a maximum axial force capacity of 300 N with good sensor characteristics.

Despite significant advances in metallurgy and the potential to create high and very high-strength steel, all international specifications for steel design provided little information about the limits of slenderness for high-strength steel sections (HSSs) and didn’t give anything about the design of very high-strength steel sections (VHSSs). The American structural steel design specification covers circular hollow sections (CHS) of steel grades up to S690, while it isn't in ANSI/AISC 360-16 and ASTM A514/A514M. Euro code EN 1993-1-1 can be applicable only to steel grades up to S460. EN 1993-1-3 and EN 1993-1-12 contain supplementary rules for cold-formed members and HSS (S460- S700), respectively. Though ductility requirements for (HSS) are specifically established in EN 1993-1-12, it is largely a continuation of the normal-strength-steel design procedures standardized in EN 1993-1-1, where (HSSs) are largely treated as normal-strength steels in these rules, and the same design approaches are used. The behavior of high and very high-strength steel circular hollow sections under axial compression load is studied in this research. A total of 16 nonlinear finite-element (FE) models were generated to replicate stub column tests that were experimentally tested by others in previous research. Hence, a parametric study is conducted using forty FE models developed to investigate the local buckling behavior under various slenderness ratios comprehensively. The developed models cover slenderness ratios ranging from 20 to 1226 and steel grades S460 and S1100 with yield stress equal 460 MPa and 1152 MPa, respectively. The FE results were combined with 105 previously collected experimental results to assess the applicability of existing codified design methodologies in the Euro code and the North American codes of cold-formed CHS. Based on the results of this study, new cross-sectional slenderness limits and new design equations for more efficient simple designs were presented for high and very-high strength steel circular hollow sections and Compared with the results of experimental tests and FE models.

Selective Laser Melting (SLM) is a complex additive manufacturing process that requires precise control of thermal conditions to ensure the quality and reliability of produced parts. The main challenge lies in accurately predicting the thermal behavior during SLM, which is influenced by rapid heating and cooling cycles, high thermal gradients, and temperature-dependent material properties. This study addresses this challenge by developing a comprehensive thermal model for the SLM process of 316L stainless steel (316L SS) and Ti6Al4V titanium alloy using Finite Element Analysis (FEA) in Abaqus. The model incorporates temperature-dependent material properties and phase transformations to simulate the temperature distribution and thermal history during SLM. To validate the model, experimental studies were conducted using custom-designed argon chambers and stainless-steel powder. The experimental results showed strong agreement with the simulated melt pool dimensions and thermal histories, confirming the model's accuracy. Key findings include the model's ability to predict the effects of varying processing parameters such as laser power and scanning speed on thermal behavior and melt pool characteristics. This validated model serves as a valuable tool for optimizing SLM processing parameters, enhancing the un-derstanding of thermal phenomena in additive manufacturing, and improving the quality and reliability of manufactured parts. Due to budget constraints, experimental validation was initially performed only on 316L SS. This approach allowed for the tuning of the finite element model before extending its application to Ti6Al4V. The successful validation with 316L SS provides a solid foundation for applying the model to more challenging materials like Ti6Al4V, ensuring cost-effectiveness and safety in initial experimentation. The novelty of this research lies in its detailed and validated thermal model, which bridges the gap between experimental and numerical approaches in SLM. By accurately simulating and validating the thermal processes involved in SLM, this study contributes to the advancement of additive manufacturing technologies and offers practical insights for industrial applications.

The rehabilitation of the road embankments alongside the irrigation canal, which is constructed on a Bangkok soft clay foundation, has resulted from land use growth for several decades. As a result, the embankment is always confronted with the problem of instability. Numerous articles have demonstrated that rapid drawdown of the water level in the canal could be one of the most significant reasons, whereas vehicle cyclic loading may potentially contribute to some effect of the embankment failure. To explore and assess the effects of the influence factors, the finite element method (FEM) and conventional and dynamic triaxial approaches were employed. The study also investigated the consequences of varying thicknesses of soft clay and cyclic loading with different magnitudes and frequencies. Consequently, cyclic loading can lead to an augmentation in strain distribution and excess pore water pressure. Likewise, more significant deformation and excess pore water pressure were induced by a lower frequency and deeper thickness of soft clay compared to a higher frequency and thinner thickness. In brief, vehicle repetitive loading is one of the primary factors contributing to embankment failure, with the threshold stress being approximately three-fourths of the undrained shear strength. In contrast, threshold strain is approximately one to two-fold of the monotonic strain condition.

Abstract: This paper outlines the methodology and results for a two species finite volume scalar computational drug transport model developed for simulating the mass transport of Poly(lactic-co-glycolic acid (PLGA) ) from a half-embedded single strut implanted in a coronary arterial vessel wall. The mathematical drug transport model incorporates the convection-diffusion equation in scalar form (dimensionless) with a two species (free-drug and bound-drug) mass transport setup including reversible equilibrium reaction source terms for the free and bound-drug states to account for the pharmaco-kinetic reactions in the arterial wall. The relative reaction rates of the added source terms control the interconversion of drug between the free and bound-drug states. The model is solved by a 2-D finite-volume method for discretizing and solving the free and bound drug transport equations with anisotropic vascular drug diffusivities. This model is an improvement over our previously developed model using the finite-difference method. A dimensionless characteristic scaling pre-analysis was conducted a priori to evaluate the significance of implementing the reaction source terms in the transport equations. This paper reports the findings of an investigation of the interstitial flow profile into the arterial wall and the free and bound drug diffusion profiles with a parametric study of varying polymer drug concentration (low and high), tortuosity, porosity, and Peclet and DamKöhler numbers over the course of 400 hours (16.67 days). The results also reveal how a single species drug delivery model that neglects both a reversible binding reaction source term and the porosity and tortuosity of the arterial wall cannot accurately predict the distribution of both the free and bound drug.

The combination of interstitial hyperthermia treatment (IHT) with high dose rate brachytherapy (HDR-BT) for prostate cancer treatment and has the potential to improve clinical outcome, since it highly enhances the efficiency of cell kill, especially when applied simultaneously. Therefore, we have developed the ThermoBrachy applicators. To effectively apply optimal targeted IHT, treatment planning is considered essential. However, treatment planning in IHT is rarely applied since it is regarded difficult to accurately calculate the deposited energy in the tissue in a short enough time for clinical practice. In this study, we investigated various time-efficient methods for fast computation of the electromagnetic (EM) energy deposition resulting from the ThermoBrachy applicators. Initially, we investigated the use of an electro-quasistatic solver. Next, we extended our investigation to the application of geometric simplifications. Furthermore, we investigated the validity of the superpositioning principle, which can enable adaptive treatment plan optimization without the need for continuous recomputation of the EM field. Finally, we evaluated the accuracy of the methods by comparing them to the golden standard Finite-Difference Time-Domain calculation method using gamma-index analysis. The simplifications considerably reduced the computation time needed, improving from >12 h to a few seconds. All investigated methods showed excellent agreement with the golden standard by showing a >99% passing rate with 1%/0.5 mm Dose Difference and Distance-to-Agreement criteria. These results allow the proposed electromagnetic simulation method to be used for fast and accurate adaptive treatment planning.

The electrical motor design requires a lot of work and resources. In the field, motor designers need to decide on competitive motor sizing quickly to compete with other motor suppliers. Generally, it requires expensive FEM S/W to get accurate motor sizing results, but buying and maintaining many licenses is costly. Moreover, it needs some patience to get the result from FEM analysis. In this paper, the motor sizing technique using an existing production motor is presented to respond to urgent requests from customers without using FEM analysis. In order to enhance the fidelity of the result, magnetic flux loss by magnet coating and non-linear characteristics are considered during the motor sizing process. The proposed sizing method was verified by comparison to the FEM analysis and test result and showed reasonable confidence in them. Also, this method has the substantial advantage of outputting accurate results instantly without taking any time. It helps with the modification design of electrical motors without using expensive FEM S/W and a certain level of skill or experience.

Large values and gradients of stresses and deformations, triggering concentrations of stresses and deformations, arise in the corner areas of a structure. The action of forced deformations, leading to the finite rupture of the contact between the elements of a structure, also triggers the concentration of stresses, while the rupture reaches an irregular point, a line on the area boundary. The theoretical analysis of the stress-strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous forced deformations is reduced to the study of singular solutions to the homogeneous problem of the elasticity theory that has power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the zone, that is close to the vertex of the angular cutout in the area boundary, has substantial deformations, rotations, and it corresponds to rising values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighbourhood of the irregular point of the boundary. For such areas, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of forced deformations. This will allow analyzing the effect of relations between orders of values of deformations, rotations, and forced deformations on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relations of deformation orders, rotations, forced deformations on the form of the equilibrium equation in the polar coordinate system for a V-shaped area under the action of forced temperature-induced deformations with regard for the geometrical non-linearity and physical linearity.

Robots in space are necessarily extremely light and lack structural stiffness resulting in natural frequencies of resonance so low as to reside inside the attitude controller’s bandwidth. A variety of input trajectories can be used to drive a controller’s attempt to ameliorate the control-structural interactions where feedback is provided by low-quality, noisy sensors. Traditionally, step functions are used as the ideal input trajectory. However, step functions are not ideal in many applications, as they are discontinuous. Alternative input trajectories are explored in this manuscript and applied to an example system that includes a flexible appendage attached to a rigid main body. The main body is controlled by a reaction wheel. The equations of motion of the flexible appendage, rigid body, and reaction wheel are derived. A feedback controller is developed to account for the rigid body modes. Additional filters are added to compensate for the system’s flexible modes. Sinusoidal trajectories are autonomously generated to feed the controller. Whiplash compensation is additionally implemented for comparison. The control method without random errors with the smallest error is the sinusoidal trajectory method, which showed a 97.39% improvement when compared to the baseline response when step trajectories were commanded, while the sinusoidal method was inferior to traditional step trajectories when sensor noise and random errors were present.

Vibration suppression in a field of frequencies and the creation of band gaps which do not allow the propagation of the waves is studied in this paper by means of microstructures designed through topology optimization. Topology optimization is formulated in frequency domain. Band gap design is based on Floquet-Bloch theory and genetic optimization. The result is appealing in view of modern 3D printing techniques.

High temperature (HT) geothermal wells can provide green power 24h a day 7 days a week. Harsh environmental and operational conditions, long-term durability requirements of such wells require special cementitious composites for well construction. This paper reports a comprehensive assessment of geothermal cement composites in cyclic pressure function laboratory tests, field exposures in an HT geothermal well (300-350oC) as well as a numerical model to complement the experimental results. Performances of calcium-aluminate-cement (CAC)-based composites and calcium free cement were compared against reference Ordinary Portland Cement (OPC)/silica blend. The stability and degradation of the tested materials was characterized by crystalline composition, thermo-gravimetric, and elemental analyses, morphological studies, water-fillable porosity, and mechanical properties measurements. All CAC-based formulations outperformed the reference blend both in the function and exposure tests. The reference OPC/silica lost its mechanical properties during the 9-month well exposure through extensive HT carbonation, while properties of the CAC-based blends improved over that period. The Modified Cam-Clay (MCC) plasticity parameters of several HT cement formulations were extracted from triaxial and Brazilian tests and verified against the experimental results of function cyclic tests. These parameters can be used in well integrity models to predict field-scale behavior of the cement sheath under geothermal well conditions.

Let $f\left(1\right)=1$ , and let $f(n+1)=2^{2^{f\left(n\right)}}$ for every positive integer n. We consider the following hypothesis: if a system S ⊆ {x_i · x_j = x_k : i, j, k ∈ {1, . . . , n}} ∪ {x_i + 1 = x_k : i, k ∈{1, . . . , n}} has only finitely many solutions in non-negative integers x₁, . . . , x_n, then each such solution (x₁, . . . , x_n) satisfies x₁, . . . , x_n ≤ f (2n). We prove: (1) the hypothesisimplies that there exists an algorithm which takes as input a Diophantine equation, returns an integer, and this integer is greater than the heights of integer (non-negative integer, positive integer, rational) solutions, if the solution set is finite; (2) the hypothesis implies that there exists an algorithm for listing the Diophantine equations with infinitely many solutions in non-negative integers; (3) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many rational solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has a rational solution; (4) the hypothesis implies that the question whether or not a given Diophantine equation has only finitely many integer solutions is decidable by a single query to an oracle that decides whether or not a given Diophantine equation has an integer solution; (5) the hypothesis implies that if a set $\mathfrak{M}$ ⊆ has a finite-fold Diophantine representation, then $\mathfrak{M}$ is computable.

In this paper, we extend the KdVSKR equations in (1+1)-dimension and (2+1)-dimension to fractional KdVSKR equations with modified Riemann-Liouville derivative. The (2+1)-dimensional KdVSKR equation, which is a recent extension of (1+1)-dimensional KdVSKR equation, can model the resonances of solitons in shallow water. By means of the Hirota bilinear method, finite symmetry group method and consistent Riccati expansion method, many new interaction solutions have been derived. Soliton-cnoidal interaction solution of the (1+1)-dimensional fractional KdVSKR equation has been derived for the first time. For the (2+1)-dimensional frac-tional KdVSKR equation, two-wave interaction solutions and three-wave interaction solutions, including dark-soliton-sine interaction solution, bright-soliton-elliptic interaction solution, and lump-hyperbolic-sine interaction solution, have been derived. Impact of the fractional order on the shapes of these solutions has been illustrated by figures. Three-wave interaction solutions of fractional systems have not been reported in the existing references. The research idea in this paper can be applied to other fractional differential equations.

Recently, more wind turbine systems are being installed in deep waters far from the coast. Several concepts of floating wind turbine systems (FWTSs) are developed, among which the semisubmersible platform, due to its applicability in different water depths, good hydrodynamic performance, and facility in the installation process, constitutes the most explored technology compared to the others. However, a significant obstacle to the industrialization of this technology is a design of a cost-effective FWTS, which can be achieved by optimizing the geometry, size and weight of the floating platform, along with the mooring system. This is only possible by selecting a method capable of accurately analyzing the FWTS coupled hydro-aero-structural dynamics at each design stage. Accordingly, this paper aims at providing a detailed overview of the most common coupled numerical and physical methods, including their basic assumptions, formulations, limitations, and costs, used for analyzing the dynamics of FWTSs, mainly those supported by a semisubmersible, to assist the choice of the most suitable method at each design phase of FWTSs. Finally, the article discusses possible future research to address challenges in modeling FWTSs dynamics that persist to date.