Equation Method Research Articles

Dynamic modeling method and parameter calibration of subarea thin-layer elements in bolted connection area of diaphragm coupling

Abstract Aiming at the finite element modeling problem on the dynamic characteristics of multi-layer elastic diaphragm bolted joints, and adopting the equivalent modeling method of subarea thin-layer elements, a parameter identification method that can accurately and efficiently identify the material parameters of each area of subarea thin-layer elements is proposed. Taking the diaphragm coupling in the marine propulsion shaft system as an example, the accuracy of the simplified model is verified by comparing the dynamics characteristics of the vibrational mode, driving point mechanical impedance, and vibration level drop between test and simulation. The variation of material parameters in each region under different bolt preloads was studied, and the effects of different material parameters on the dynamic properties were analyzed, in which the elastic modulus had a greater effect on the model dynamic characteristics, while Poisson's ratio and density had a smaller effect. The research results show that the subarea thin-layer element modeling method can effectively simplify the dynamic modeling method of the diaphragm coupling under the consideration of bolt preload, and the parameter identification based on the multi-objective genetic algorithm can accurately identify the material parameters of each area of the subarea thin-layer element, which can be used to analyze the dynamic characteristics of the multilayered elastic diaphragm bolted couplings.

Rheological and mechanical properties of self-compacting concrete with recycled coarse aggregate from the demolition of large panel system buildings

Abstract Self-compacting concrete (SCC), which can be placed and consolidated under its weight without any vibration effort, was first developed in 1988 to achieve durable concrete structures. Since then, a lot of research has been conducted in order to reduce the consumption of raw materials in SCC. Although coarse aggregate and design methods are known to influence concrete properties, there are still knowledge gaps that need to be filled. This study uses a new source of recycled coarse aggregate (RCA), namely the concrete panels of old large panel system buildings demolished in urban areas. The aim of the study is to verify the effect of this aggregate on the rheological and mechanical properties of SCC. To enhance the properties of SCC, the modified equivalent mortar volume (mEMV) method of designing a concrete mix was used. It has not been verified before for SCC, and a literature review suggests it has the potential to eliminate the drawbacks of ordinary equivalent mortar volume methods. The SCC that was used in the study is characterized by having a high viscosity and an average consistency. The hardened SCC used in the research was highly impacted by its mix design and RCA content. Both compressive strength and abrasion resistance decreased when the RCA content increased. However, using the mEMV method resulted in a 10 and 1% improvement in compressive strength and abrasion resistance, respectively.

Theoretical and Experimental Investigation of Critical Buckling Load of Combined Columns

The work done in this research is dedicated to compute the critical buckling load of combined columns. This is performed using theoretical and experimental analyses. The combined column is made of two materials, namely copper and aluminum alloys. The theoretical approach involves numerical analysis using ANSYS and analytical analysis using the equivalent stiffness method. The study determines the critical buckling load by considering many parameters. These parameters include lengths of copper and aluminum in the combined columns, cross-sectional geometries (square, circle, and hexagon), and boundary conditions. The experimental work is carried out using a Strut Bucking Apparatus on a combined column with circular cross-sections and different end supports. The findings show that the critical buckling loads achieved from numerical and analytical analysis are in good agreement with those obtained from experimental analysis. It is found that the critical buckling load increases with increasing the length of copper in the combined column and with more restrictive end supports. There is a good match of critical buckling load between those achieved from the equivalent stiffness method and ANSYS model for any considered cross-sectional geometries (square, circle, and hexagon) and two types of support (fixed-fixed and fixed-pinned). The results reveal that the combined columns with square cross-sections have higher critical buckling loads than those with circular or hexagonal cross-sections. The highest percentage errors of critical buckling load between the experimental method and theoretical methods (equivalent stiffness method and ANSYS models) are (-13.120, -12.768, and -12.453) % and (-13.083, -18.039, and -19.052) % for pinned-pinned, fixed-pinned, and fixed-fixed columns respectively.

Fatigue Assessment of Rib–Deck Welded Joints in Orthotropic Steel Bridge Decks Under Traffic Loading

Rib–deck (RD) welded joints in orthotropic steel bridge decks are prone to different fatigue crack mechanisms. Standard fatigue design methods are inadequate for some of these mechanisms under multiaxial non-proportional loading conditions. This study presents a framework to assess fatigue damage at RD welded joints, considering the different crack mechanisms based on the equivalent structural stress method and its extension to multiaxial non-proportional fatigue, which is the path-dependent maximum stress range (PDMR) cycle counting algorithm. The method is validated for uniaxial loading by using experimental data from the literature. Additionally, non-proportional fatigue damage at RD welded joints of a suspension bridge girder is investigated under simulated random traffic loading. The analyses reveal the limitations of the nominal stress approach to account for complex stress field variations. The PDMR method, more suited to capture the stress path dependency of non-proportional fatigue damage than the hot spot and critical plane-based methods, predicts higher fatigue damage. A comprehensive fatigue test campaign of full-scale RD welded joints is necessary to better understand their fatigue behaviour under multiaxial loading. Until more experimental data are available, the PDMR method is recommended for fatigue verifications of welded RD joints as it yields safer predictions.

Based on the Thickness Equivalent basis effect decomposition method of ore separation by multi-energy X-ray transmission technology

Based on the Thickness Equivalent basis effect decomposition method of ore separation by multi-energy X-ray transmission technology

Equivalent Inclusion Method (EIM) for isotropic and anisotropic spatially oriented spheroidal inhomogeneities: A unified calculation module validated via comparisons to Finite Element (FE) simulations

This paper is centered on the Equivalent Inclusion Method due to Eshelby (Eshelby, 1957, 1959, 1961) to solve inhomogeneous ellipsoidal inclusion problems. The objective is to develop a unified EIM program for spatially oriented isotropic and anisotropic spheroids and validate each stage of the developments in a controlled and rigorous way. At first, the analytical calculations of spatial derivatives of the elliptic integrals, involved in the expression of the strain field in the isotropic infinite medium, are pushed as far as possible for an Oblate spheroid and coded as it was done by (Vincent et al., 2014) for the Prolate shape. Then, spatial orientation of the spheroid with respect to the global axis system attached to the infinite medium is introduced. Anisotropic metal inhomogeneities are finally dealt with, with the possibility to assign different crystallographic orientations. In this final configuration involving both the spatial orientation and anisotropy, three axis systems have to be managed simultaneously. Such a complexity legitimates a progressive evaluation towards this case. Thus, each new functionality introduced in the code is carefully validated by comparisons of the results to Finite Element reference solutions both inside and outside the inhomogeneity along different paths from the interface. This is done for an isotropic inhomogeneity without and with spatial orientation at first, and for an anisotropic inhomogeneity in the same way. These evaluations are presented for different shapes, aspect ratios, property contrasts. Such a complete evaluation involving at each stage various cases and examining the fields inside and outside the inhomogeneity constitutes an original contribution of the present work and allows to be confident in the proposed code (available on request). Another contribution of the paper is to analyze the influence of various factors (shape, aspect ratio, spatial orientation) on the fields distribution when both the anisotropy and the spatial orientation of the spheroidal inhomogeneity are combined. This last part illustrates also the efficiency of the EIM to deal with such analysis with both accuracy and a low calculation cost.

Equivalent radiation attenuation method for nuclear radiation field reconstruction

Equivalent radiation attenuation method for nuclear radiation field reconstruction

Rationalized equivalence method for high-velocity impacts of composite and metal panels

Rationalized equivalence method for high-velocity impacts of composite and metal panels

A novel approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity

Precise seismic fragility analysis holds significant importance in the evaluation of seismic resilience for underground structures. However, the conventional seismic fragility analysis of underground structures usually ignores the hybrid epistemic uncertainties caused by the limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states, which can inevitably cause errors in the seismic resilience evaluation of underground structures. Thus, focusing on the quantification of epistemic uncertainties, this paper aims to propose an approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity. In this approach, the analytical formulation of seismic fragility considering the fuzziness of limit states is firstly derived via adopting the entropy equivalence method. Then, the non-parametric Bootstrap method and maximum entropy principle, as well as the Copula theory are combined to establish a probability model characterizing the statistical uncertainties of both seismic demand and capacity. On this basis, the variability of failure probability of underground structures is quantified, and the envelope fuzzy seismic fragility is obtained. Moreover, the influences of the coupling effect of statistical uncertainty and fuzziness on the seismic fragility of underground structures are also analyzed in this paper. The results show that the seismic fragility of underground structures based on limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states has significant variability, and the variability degree of fragility is various under different ground motion intensities. Besides, the envelope fuzzy seismic fragility curves can effectively reflect the coupling effect of statistical uncertainty and fuzziness and adequately characterize the variability of estimated seismic fragility, which can provide a more accurate basis for seismic resilience evaluation of underground structures.

The workload analysis for the mackarel cracker industry's workers uses the full-time equivalents method

Kerupuk Ikan Tenggiri Cap Kuda Laut is one of the fish-based cracker industries. The industry is located at Pangkalan Brandan, North Sumatra, Indonesia. The fish-based cracker industry employs 15 workers and six workstations, which include fish processing stations, fish grinding stations, kneading stations, printing stations, frying stations and packing stations. According to the observations, there is an unequal division of worker, which can result in an inappropriate workload for the worker. This study aims to analyze workers' workloads as a basis for determining the optimal number of workers. The full-time equivalent (FTE) method simplifies the measurement of work by aligning the number of people required to complete a specific job with the hours of workload. The study's findings revealed that one worker at the grinding stations had an overload, three workers in fish processing, two workers in kneading, three workers in frying and printing had normal workloads. Also at the packaging station there are 3 workers with an underload

Concrete Mix Design of Recycled Concrete Aggregate (RCA): Analysis of Review Papers, Characteristics, Research Trends, and Underexplored Topics

Recycled concrete aggregate (RCA) has been widely adopted in construction and emerged as a sustainable alternative to conventional natural aggregates in the construction industry. However, the study of holistic perspectives in recent literature is lacking. This review paper aims to provide a comprehensive analysis of RCA, highlighting its properties, applications, and overall sustainability benefits to facilitate the comprehensive points of view of technology, ecology, and economics. This paper explores the manufacturing process of RCA, examines its mechanical and durability characteristics, and investigates its environmental impacts. Furthermore, it delves into the various applications of RCA, such as road construction materials, pavement bases, and concrete materials, considering their life cycle performance and economic considerations. This review reveals that there is a need for systemic data collection that could enable automated concrete mix design. The findings concerning various mix concrete designs suggest that increasing the 1% replacement level reduces the compressive strength by 0.1913% for coarse RCA and 0.2418% for fine RCA. The current critical research gaps are the durability of RCA concrete, feasibility analyses, and the implementation of treatment methods for RCA improvement. An effective life cycle assessment tool and digitalization technologies can be applied to enhance the circular economy, aligning with the United Nations’ sustainable development goals (UN-SDGs). The equivalent mortar volume method used to calculate the RCA concrete mix design, which can contain chemical additives, metakaolin, and fibers, needs further assessment.

Improved equivalent optical turbulence method for anisotropic compressible and atmospheric turbulence under different beam transmission distances

The impact of different turbulence on beams can be seen as optical distortions caused by refractive index fluctuations around vortices in turbulence. Therefore, from the perspective of transmission effects, the transmission outcomes of beam in different turbulences can be mutually equivalent. Since the mechanisms of beam propagation in compressible turbulence are not yet fully understood and the relevant theories are not well-established, a preliminary analysis of beam transmission in compressible turbulence is necessary. This analysis will help understand the medium characteristics of compressible turbulence, particularly its similarities and differences with atmospheric turbulence, before the optical effects of compressible turbulence are fully resolved. This paper establishes a connection between anisotropic atmospheric turbulence and compressible turbulence parameters by utilizing the mature solutions of beam in anisotropic atmospheric turbulence. We then employ the optical parameters of anisotropic atmospheric turbulence to represent those in compressible turbulence, leveraging existing solutions to assess beam transmission in compressible turbulence. Building upon the original equivalent method, we extend the dimension of transmission distance, ensuring that beams equivalence is maintained across different turbulence regimes. The results indicate that the equivalent method can effectively adapt to compressible turbulence. By using the equivalent structure function, it is possible to represent compressible turbulence parameters with the atmospheric refractive index structure constant. This method also works across different transmission distances. The method facilitates finding various solutions for beam in compressible turbulence.

Research on an equivalent calculation method of the sealing structure of subsea pipeline connectors based on dimensionality reduction method

For the sealing structure of subsea pipeline connectors, it is crucial to understand the maximum equivalent stress of the sealing ring, the normal force generated by the pressure effect of the internal fluid acting on the contact area of the flanges and the sealing ring, and the displacement of the flange in the pre-tightening state and the working state. This paper proposes an equivalent calculation method (ECM) to quickly compute the values of these three variables. A theoretical model for the parallel contact of the axially symmetric object and an elastic foundation is proposed based on the dimensionality reduction method and Hertzian theory. Considering the contact and structural characteristics of the flanges and the sealing ring of the sealing structure, an equivalent hollow cylinder model is introduced. By combining these two models, along with the long hollow cylinder theory, theoretical formulas for the maximum equivalent stress, the normal force, and the flange displacement in the pre-tightening state and the working state of the sealing structure are derived. In addition, finite element simulations were conducted on the sealing structure of different sizes and working states. A comparative analysis was performed between the simulation results and the theoretical formulas results. The results show that, within the yield strength of the sealing ring, the maximum relative deviation of the three theoretical formulas is less than 10%. The theoretical formulas can be used for the design and engineering application of the sealing structure of subsea pipeline connectors.

A Literature Review on Numerical Simulation of Thermal Anti-Icing

This paper reviews the numerical simulation method for thermal anti-icing. Typically, the numerical study of an anti-icing system involves a coupled simulation of various physical processes: airflow, droplet flow, thin water film flow on the wall, and heat conduction within the solid wall. Airflow is commonly simulated using the Reynolds-Averaged Navier–Stokes method, while droplet flow can be modeled using either the Eulerian or Lagrangian approach. For simulating water film flow, there are three primary models: the Messinger model, the SWIM model, and the Myers model. The heat transfer process within the solid wall can be coupled with the external air/droplet and film flow using either a tight-coupling or a loose-coupling method. When simulating an electrothermal anti-icing system, methods such as the equivalent heat conductivity scheme or shell conduction method are employed to handle heat conduction in multi-layer thin walls. To improve the accuracy of thermal anti-icing simulations, additional research is still necessary, focusing on studies on rivulet flow, bead flow, and the heat convection coefficient on the system’s wall.

Analysis of the Influence of Excavated Soil Sand Characteristics on the Rheological and Mechanical Properties of Hydraulic Mortars

This work investigates the effects of substituting natural sand with excavated soil sand in the formulation of hydraulic mortar developed from a self-compacting concrete (SCC). Four excavated soil sand deposits were studied to assess their physicochemical properties. Subsequently, a reference mortar (RM) was designed using the concrete equivalent mortar method. Furthermore, the effect of incorporating 30% of excavation soil sand under different moisture conditions (natural storage conditions, dry and saturated surface dry state) on the properties of mortar is studied. Spreading tests were carried out to observe how the rheological properties evolve over time. The study includes compressive and flexural strength tests at 2, 7, 14 and 28 days. The results showed that some sands had densities similar to those of natural alluvial sand, while others had lower densities. Water absorption values varied considerably from one sand to another, with some showing values ranging from 1% to 6%, while other sands had values of up to 10%. The results of spreading tests indicate that mortar made with sand in a saturated dry-surface state is more fluid than mortar made with sand in a dry state. Under all conditions, all mortars lose their fluidity over time. The variation in compressive strength among all excavated soil sand mortars compared to the reference mortar remained below 10% at 2 and 28 days, except for one sand with a high clay content. The incorporation of excavated soil sand at this percentage as a substitute for river sand led to an enhancement in the flexural strength of the mortar, with improvements of 40% and 50% observed for certain types of excavated sand. The statistical study revealed a strong relationship between the properties of the sand (in particular, the fines content and their nature, as well as the sand skeleton) and its saturation state, the flowability and the compressive strength of the mortar.

The Effect of BEOL Design Factors on the Thermal Reliability of Flip-Chip Chip-Scale Packaging

With the development of high-density integrated chips, low-k dielectric materials are used in the back end of line (BEOL) to reduce signal delay. However, due to the application of fine-pitch packages with high-hardness copper pillars, BEOL is susceptible to chip package interaction (CPI), which leads to reliability issues such as the delamination of interlayer dielectric (ILD) layers. In order to improve package reliability, the effect of CPI at multi-scale needs to be explored in terms of package integration. In this paper, the stress of BEOL in the flip-chip chip-scale packaging (FCCSP) model during thermal cycling is investigated by using the finite-element-based sub-model approach. A three-dimensional (3D) multi-level finite element model is established based on the FCCSP. The wiring layers were treated by the equivalent homogenization method to ensure high prediction accuracy. The stress distribution of the BEOL around the critical bump was analyzed. The cracking risk of the interface layer of the BEOL was assessed by pre-cracking at a dangerous location. In addition, the effects of the epoxy molding compound (EMC) thickness, polyimide (PI) opening, and coefficient of thermal expansion (CTE) of the underfill on cracking were investigated. The simulation results show that the first principal stress of BEOL is higher at high-temperature moments than at low-temperature moments, and mainly concentrated near the PI opening. Compared with the oxide layer, the low-k layer has a higher risk of cracking. A smaller EMC thickness, lower CTE of the underfill, and larger PI opening help to reduce the risk of cracking in the BEOL.

Hybridizing Fabrications of Gd-CeO2 Thin Films Prepared by EPD and SILAR-A+ for Solid Electrolytes

Thin films of gadolinium-doped ceria (GDC) nanoparticles were fabricated as electrolytes for low-temperature solid oxide fuel cells (SOFCs) by combining electrophoretic deposition (EPD) and the successive ionic layer adsorption and reaction-air spray plus (SILAR-A+) method. The Ce1−xGdxO2−x/2 solid solution was synthesized using hydrothermal (HY) and solid-state (SS) procedures to produce high-quality GDC nanoparticles suitable for EPD fabrication. The crystalline structure, cell parameters, and phases of the GDC products were analyzed using X-ray diffraction. Variations in oxygen vacancy concentrations in the GDC samples were achieved through the two synthetic methods. The ionic conductivities of pressed pellets from the HY, SS, and commercial G0.2DC samples, measured at 150 °C, were 0.6 × 10−6, 2.6 × 10−6, and 2.9 × 10−6 S/cm, respectively. These values were determined using electrochemical impedance spectroscopy (EIS) with a simplified equivalent circuit method. The morphologies of G0.2DC thin films prepared via EPD and SILAR-A+ processes were characterized, with particular attention to surface cracking. Crack-free GDC thin films, approximately 730–1200 nm thick, were successfully fabricated on conductive substrates through the hybridization of EPD and SILAR-A+, followed by hydrothermal annealing. EIS and ionic conductivity (1.39 × 10⁻⁹ S/cm) measurements of the G0.2DC thin films with thicknesses of 733 nm were performed at 300 °C.

A Crack‐Length Control Technique for Phase‐Field Fracture in FFT Homogenization

ABSTRACTModeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase‐field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of jumps in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase‐field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap‐backs during the unstable propagation phases. The method is derived for FFT‐based solvers in order to exploit its very high numerical performance in micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress‐strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J‐integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as a function of the concretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.

Coupling Fully Staggered Grids via Numerical Filtering for Wave Propagation Simulation

The fully staggered grid (FSG) combines multiple standard staggered grids (SSGs) to simulate seismic wave propagation in anisotropic elastic media. However, its accuracy is contingent upon the wavefield’s consistency and continuity across multiple sets of SSGs. In isotropic or weakly anisotropic media, decoupling or weak coupling between the SSGs can lead to wavefield discontinuities at adjacent grid points in the diagonal direction. Issues such as inconsistent source activation, medium parameter discontinuities, and different numerical treatments of boundary conditions over multiple sets of SSGs can exacerbate these problems. While previous methods, such as FD-consistent point source technique and equivalent medium parameterization methods, have partially addressed these issues, they do not completely solve the problem. This study, drawing inspiration from numerical damping techniques used in collocated-grid finite-difference schemes to eliminate odd-even oscillations, introduces an explicit filter operator along the diagonal direction of the FSG. This approach ensures wavefield consistency and continuity across multiple SSGs, improving the accuracy of the FSG scheme. Although this method increases computational costs, it is essential for reliable seismic modeling in anisotropic media.

Seismic Mitigation Effect and Mechanism Analysis of Split Columns in Underground Structures in Sites with Weak Interlayers

The seismic damage of underground structures has been extensively investigated, and it has been demonstrated that underground structures located at weak interlayer sites are more prone to damage. In this study, a two-story two-span rectangular frame subway station structure is analyzed. A two-dimensional soil-underground structure model is developed using the large-scale finite element analysis software ABAQUS. The equivalent linear soil-underground structure dynamic time-history analysis method is employed to examine the seismic response of underground structures at weak interlayer sites. Variations in the thickness and shear wave velocity of the weak interlayer soil are analyzed. The seismic mitigation effects of split columns and prototype columns in underground structures at weak interlayer sites are systematically compared. The findings indicate that the relative displacement and internal force of key structural components significantly increase when the weak interlayer intersects the underground structure. Furthermore, as the thickness of the interlayer increases, the displacement and internal force also escalate. When the thickness of the weak interlayer remains constant and the shear wave velocity decreases, the relative displacement and internal force of the key structural components gradually intensify. Replacing ordinary columns with split columns substantially reduces the internal force of the middle column, providing an effective seismic mitigation measure for underground structures.