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This study investigates the analytical approach of web reinforcement techniques, including high-strength concrete and laced reinforcement, to enrich improvement for the structural behavior of these beams. The analysis compares an unmodified cellular beam (LB1) with a web-reinforced beam (LB2), including the improvements in load-carrying capacity. The study considers the effects of reinforcement on critical design limit states, such as flexural strength, Vierendeel bending, web post-buckling, and shear resistance. The outcomes reveal significant enhancements in LB2’s structural behavior, with over a 100% increase in flexural strength and local axial force capacity and a 165% increase in web post-buckling strength. This research validates the effectiveness of web reinforcement techniques in concentrating on the limitations of cellular beams and maximizing their potential in structural applications.

Hydraulic axial force is an important parameter of the performance of centrifugal pump. It strongly affects the operation stability and the life-time of thrust bearing. Under the influence of flow pressure distribution, the hydraulic axial force of centrifugal pump has mainly two parts. One is the force inside impeller while the other is the force in clearance. In this case, the situation is more complex because the pump operates with varying-speed. Under the influence of rotation speed, pump head and minimum clearance width, the variation law of clearance axial force is still not fully understood. Therefore, the orthogonal experiment is conducted based on Large Eddy Simulation (LES). The local flow and hydraulic axial force in impeller shroud clearance is mainly studied. Results show that the pressure difference between impeller inlet and outlet will strongly impact the pressure distribution in clearance. Then, it affects the clearance axial force. The rotation speed and pump head are proved influential. However, range analysis shows that the minimum clearance width is the most dominant factor. It can somehow adjust the pressure distribution in clearance. The geometric design of impeller clearance will be important in reducing hydraulic axial force especially for varying-speed centrifugal pumps.

Due to the harsh service environment and multiple loads, studying the nonlinear vibration characteristics of rotating blades under complex loads is necessary. The new axial force model assumed as a combined force including the non-uniform aerodynamic force in the tip clearance and blade-casing local rubbing force is proposed for the first time in this paper. The nonlinear analysis of a rotating pre-twisted composite blade reinforced with functionally graded graphene platelet (FGGP) is investigated under axial and transverse excitations. The blade is treated as FGGP-reinforced rotating twisted cantilever plate. The transverse excitation caused by subsonic airflow is derived by using the vortex lattice method. The blade-casing local rubbing and non-uniform axial force dynamic change when the blade is rotating. Based on von-Karman nonlinear geometric assumptions and Lagrange equation, the governing equations of motion for the FGGP-reinforced rotating twisted plate are derived. The averaged equations under the case of primary resonance and 1:2 internal resonance are obtained by the multiple scale method. Comparisons of frequencies and modes in the present method are carried out. The results are in good agreement with other literature. The amplitude–frequency and amplitude–force curves, bifurcations, and chaotic motions of the FGGP-reinforced rotating twisted cantilever plate under axial and transverse excitations are discussed. The results show that the nonlinear vibrations are complex when 1:2 internal resonance and primary resonance of the FGGP-reinforced rotating twisted composite blade occur. The amplitude of the blade is higher with the bigger axial force. At the same time, with the increase of axial force and incoming flow speed, the motion of the blade changes from periodic to chaotic. The interesting phenomena of inverse period-doubling bifurcations are found.

The variable cross-section arch is widely used in practical engineering because of its beautiful arc and excellent mechanical properties. However, there is still no systematic and comprehensive study on the out-plane buckling of variable cross-section arches. In view of this, this paper is focused on the elastic analytical research of out-plane buckling of arches with variable cross-sections under a uniformly distributed radial local load. The pre-buckling and out-plane buckling behavior of a variable cross-sectional arch under an external load is quite different from that of an arch with a uniform cross-section. Castigliano’s second theorem is used to establish pre-buckling force method equilibrium equations for variable cross-sectional arches under a uniformly distributed radial local load, and corresponding analytical solutions of normal stress, axial compression, and the bending moments are obtained. Based on the energy method and the Ritz method, analytical solutions of the critical load for the elastic out-plane buckling of arches with variable cross-sections are derived. Comparisons with ANSYS results indicated that the analytical solutions are able to accurately predict the pre-buckling internal forces and critical out-plane buckling load of variable cross-section arches subjected to a uniformly distributed radial local load. It is found that the internal forces and the out-plane buckling load of an arch are significantly affected by the variation of cross-sectional height. As the ratio of the arch’s cross-sectional height increases, the bending moment decreases, and the axial force and critical out-plane buckling load increase. Analytical solutions of pre-buckling internal force and critical out-plane buckling load problems for arches with variable cross-sections have a wider significance since they can provide an effective explicit analytic method for the optimal design of arch structures.

The unsteady forces acting on a body depend strongly on the local flow structures such as vortices. A quantitative understanding of the contribution of these structures to the instantaneous overall force is of fundamental significance. In the present study, a three-dimensional (3-D) vortex force map (VFM) method, extended from a two-dimensional (2-D) one, is used to provide better insight into the complex 3-D flow dynamics. The VFM vectors are obtained from solutions of potential equations and used to build the 3-D VFMs where the critical regions and directions associated with significant positive or negative contributions to the forces are identified. Using the existing velocity/vorticity field near the body, these VFMs can be used to obtain the body forces. A decomposed form of the force formula is also derived to separate the correction term contributed from the uncaptured vortices (close to or far away from the body). The present method is applied to the starting flow of a delta wing at high angle of attack, where LEVs are enhanced and stabilized by an axial flow effect. The analogy between the normal force of a slender delta wing and that of a 2-D flat plate with a steadily growing span is demonstrated via the VFM analysis. We find, for this application, that the force evolution exhibits some similar behaviour to a 2-D airfoil starting flow and, surprisingly, the force contribution mainly comes from the conical vortex sheet rather than the central core. Moreover, a quantitative understanding of the influence of LEVs in different evolution regimes on the body force is demonstrated.

Frequent accidents may happen during the string run-down and pull process due to the lack of accuracy in the prediction of string force analysis. In order to precisely predict the completion string axial force in horizontal wells, a new model is established, and an in-house software has been developed. The model aims to predict the multiple local resistances that occur at different points on the completion string, which makes up for the technical defects of the commonly used software. It can calculate resistance at different points of the string, which will lead to varying hook load amplification. This method can also predict the axial force of the completion string. By changing the hook load, location, and direction, the resistance can be determined more accurately. Based on the calculation and analysis, the relationship between local resistance, the blocking point, and the amplification factor is also obtained. Furthermore, this model is used to analyze the local resistance of a horizontal well with multiple external packers in the low-permeability Sadi Reservoir of Halfaya Oilfield, Iraq. The recorded data from in-site operations are compared with the predicted results from this model. The results show that the relative errors between the recorded data and model calculation are within the range of 10%, which indicates that the calculated values are reliable. Meanwhile, the results indicate the success of the subsequent completion design and the construction of the oilfield.

There are an increasing number of cases wherein the soil around a tunnel is immersed in water, which adversely affects the tunnel. To study the influence mechanism of local immersion of loess stratum on metro shield tunnel in detail, a similarity model test and numerical simulation were used in this study. These were used to investigate the stress and deformation of tunnel lining and stratum and surface settlement after a local soil collapse in the tunnel, and the mechanical mechanism that causes this effect. Further, the influences of different methods of water immersion on the tunnel lining were studied using numerical simulation. The results showed that the larger the collapsing area, the larger the bending moment and the axial force increment of the tunnel lining and the surface settlement; the bending moment and axial force near the side of the collapsing area were larger than those of the non-wet side. Vertical stress in the collapsible area was reduced, while the vertical stress of the non-collapsible soil on both sides of the collapsible area was increased due to the transmission of stress. When the water immersion area was the same, different water immersion methods also made the internal force of the tunnel lining slightly different; however, the difference was not obvious.

This paper presents a comparison of two variants of an axial flux magnetic gear (AFMG), namely, with integer and fractional gear ratios. Based on calculations derived with the use of three-dimensional numerical models, the torque characteristics of the analyzed AFMGs are computed and verified on a physical model. The greatest emphasis is put on the detailed decomposition and analysis of local forces in modulator pole pieces (also used in the structural analysis) within the no-load and maximal load conditions. The authors also describe the unbalanced magnetic forces (UMF) in the axial and radial directions resulting from the construction of the considered AFMGs variants, and their possible effects in the context of the use of additive manufacturing (AM) in prototypes. The paper also proposes an effective method for limiting the axial strain by using the asymmetry of the air gaps, which slightly reduces the torque transmitted by AFMGs. Finally, a static strength analysis was presented that allows us to assess the effects of local forces in the form of modulator disc deformation for selected cases of air gap asymmetry.

In this study, elastic metamaterial sandwich plates with axially deformed Timoshenko beam cores, considering both the out-of-plane and in-plane deformations of the face plates, are designed and the vibration band-gap properties are explored. The beam cores act as local resonators that can bear axial force, bending moment and shearing force. The finite element method (FEM) and the spectral element method (SEM) are combined to create the finite/spectral element hybrid method (FE-SEHM) for establishing the dynamic model and calculating the frequency response functions (FRFs) of the elastic metamaterial sandwich plate with axially deformed beam cores. It is observed that the metamaterial sandwich plate possesses both the axial and transverse vibration band-gaps of the beams, and the two kinds of band-gaps are independent. Compared with the metamaterial sandwich plates with rod cores, those with axially deformed beam cores have more extensive application ranges for vibration reduction.

The interest in phononic crystals and acoustic metamaterials has been an intensive subject of research in recent years. Finding a robust way to significantly expand or actively control the bandgap has received extensive attention. In this study, we propose a prestressed metamaterial beam attached with multiply local resonators connected by actively tunable piezoelectric springs. The Euler–Bernoulli beam theory and Timoshenko beam theory are applied in the theoretical analysis of the system. Further, the spectral element method is utilized to analytically compute the dispersion relation and transmission ratio and excellent agreement with reference to the benchmark is reported. The influences of an external axial force on the bandgap range and attenuation behavior are further studied. Subsequently, the effect of resonator number and mass on the local resonance bandgap structure is investigated in two parametric studies. The active control of bandgap range and frequency is then verified. By analyzing frequency response function, the tunable transmission ratio of a supercell can be observed. To conclude, this paper not only provides a guideline for designs of wave attenuation with multiple frequency regimes in a one-dimensional system, but it can also be extended to sub-wavelength wave manipulation designs.