Minimum Potential Energy Theory Research Articles

Settlement and stress analysis in stabilized slab- and pile-supported embankment based on double-equal settlement plane

PurposeThe soft stabilized slab and pile-supported (SSPS) embankment is an improvement technique to increase the efficiency of resources in road construction. To capture the effects of stabilized slabs on the stress transfer mechanism, the differential settlements and the lateral displacement of the embankment completely. A theoretical model of SSPS is proposed by considering the effect of soil arching and the interaction between the embankment fill, stabilized soil, pile, foundation soil and bearing stratum.Design/methodology/approachIn the theoretical model, the stress and strain coordination relationship of the system was analyzed in view of the minimum potential energy theory and equal settlement plane theory. Subsequently, the theoretical method was applied to field tests for comparison. Finally, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and foundation settlement were examined.FindingsIn addition to the experimental findings, the method has been revealed to be reasonable and feasible, considering its ability to effectively exploit the stabilized slab effect and improve the bearing capacity of soil and piles. An economical and reasonable arrangement scheme for the thickness and strength of stabilized slabs was obtained. The results reveal that the optimum elastic modulus was chosen as 28 MPa–60 MPa, and the optimum thickness of the stabilized slab was selected as 1.5 m–2.1 m using the parameters of field tests, which can provide guidance to engineering design.Originality/valueAn optimization calculation method is established to analyze the load transfer mechanics of the SSPS embankment based on a double-equal settlement plane. The model’s rationality was analyzed by comparing the settlement and stress concentration ratios in the field tests. Subsequently, the influence of the elastic modulus and the thickness of the stabilized slab on the stress concentration ratio and settlement were examined. An economical and reasonable arrangement scheme for the thickness and elastic modulus of stabilized slabs was obtained, which can provide a novel approach for engineering design.

Mechanics equilibrium in Tai-chi diagram

Tai chi culture has a widespread influence on the world. Tai-chi diagrams, as the symbol of Tai chi culture, express the balance between Yin and Yang through the centrosymmetric pattern, but the balance connotation of Tai-chi diagrams needs a comprehensive understanding in more aspects, e.g., the balance in mechanics. In this work, we propose a mechanics theory to investigate the intrinsic mechanism of Yin–Yang equilibrium in ancient and modern Tai-chi diagrams. The model based on the minimum potential energy theory can effectively describe the interface curves of the Yin–Yang equilibrium by modifying boundary conditions, which is proven by experiments. The results show that the balance of Tai-chi diagrams is not only manifested in its symmetrical appearance but also reflected in its intrinsic balance configuration in mechanics. The model presented herein provides a new perspective to understand the balance of Tai-chi diagrams, which may provide useful insights into the applications of Tai-chi diagrams.

Spontaneous buckling morphology transition of an elastic ring confined in an annular region constraint

This paper studies the spontaneous buckling morphology transition of an elastic ring confined in an annular region constraint. With the increase of uniform axial strain, the ring initially forms a symmetrical blister, and then the blister is compressed, spontaneously inclines and transits to the “S” shape. A theoretical framework based on the minimum potential energy theory is proposed to obtain the critical strain of morphology transition, which matches well with experimental results. The map predicting stable buckling shapes of the ring with different geometrical parameters is demonstrated, which may offer helpful guidance to practical applications, for example, the design of gear-less pump and rotary actuators.

Buckling stability analysis of underpinning piles during basement excavation beneath existing buildings

In the present paper, the pile-soil system’s total potential energy equation of underpinning piles was established based on the Winkler elastic foundation beam theory. This energy equation was used to explore the effect of basement excavation beneath existing buildings on the underpinning pile’ buckling stability. Utilizing the minimum potential energy theory, the expression of the critical buckling load for underpinning piles’ stability during the excavation project was obtained. Moreover, the influencing factors of the critical buckling load were investigated. It was found that the underpinning pile’s critical load converged with the augment of half-wave number. Moreover, the pile skin friction and deadweight had an insignificant influence on it. In addition, the critical load of underpinning piles decreased sharply with the increasing excavation depth and gradually increased with the augment of pile diameter. The results of this study provides a basis for the design of adding piles in similar projects and reduces the hidden danger of excavation instability.

Hyper-Redundant Manipulator Capable of Adjusting Its Non-Uniform Curvature with Discrete Stiffness Distribution

Hyper-redundant manipulators are widely used in minimally invasive surgery because they can navigate through narrow passages in passive compliance with the human body. Although their stability and dexterity have been significantly improved over the years, we need manipulators that can bend with appropriate curvatures and adapt to complex environments. This paper proposes a design principle for a manipulator capable of adjusting its non-uniform curvature and predicting the bending shape. Rigid segments were serially stacked, and elastic fixtures in the form of flat springs were arranged between hinged-slide joint segments. A manipulator with a diameter of 4.5 mm and a length of 28 mm had been fabricated. A model was established to predict the bending shape through minimum potential energy theory, kinematics, and measured stiffnesses of the flat springs. A comparison of the simulation and experimental results indicated an average position error of 3.82% of the endpoints when compared to the total length. With this modification, the manipulator is expected to be widely used in various fields such as small endoscope systems and single-port robot systems.

Method of determining the minimum number of stiffeners for stiffened corrugated steel walls

The ultimate shear resistance of trapezoidal corrugated steel plate shear walls (TCSPSWs) with large width-to-height ratios can be increased by adding vertical stiffeners (steel strips). However, the minimum required number of steel strip, which is significant to the practical design of the stiffened TCSPSWs, needs to be investigated. Therefore, a theoretical method of determining the number of steel strips for the stiffened TCSPSWs is introduced. Based on the orthotropic plate theory, the theoretical model of solving the elastic buckling load of the steel-strip-stiffened TCSPSWs is established by utilizing the minimum potential energy theory and Rayleigh-Ritz method. Then the established theoretical model is verified by finite element (FE) models, and the maximum elastic buckling load of the stiffened TCSPSWs is investigated. Subsequently, method of comparing the maximum critical buckling loads of the stiffened TCSPSWs with the corresponding yield loads to determine the minimum required number of steel strips is proposed. Finally, accompanied by providing several calculation examples as illustrations, the method is verified by FE elastoplastic analyses. Results indicated that the proposed method is reliable to be applied to determine the minimum required number of steel strip for the stiffened TCSPSWs in practical engineering.

Elastic buckling analysis of steel-strip-stiffened trapezoidal corrugated steel plate shear walls

The overall instability of trapezoidal corrugated steel plate shear walls (TCSPSWs), induced by out-of-plane buckling, has been a major influencing factor on its seismic performance. Steel strips are believed to be effective in restricting out-of-plane buckling and improving the seismic performance of TCSPSWs. This paper investigates the elastic buckling behavior of vertical TCSPSWs stiffened by horizontal steel strips. Theoretical model based on the orthotropic plate theory is established in this study by applying the elastically torsional-restrained edges to the TCSPSW model. Based on minimum potential energy theory and Rayleigh-Ritz method, the elastic buckling load of the stiffened TCSPSWs can be solved. Besides, the critical rigidity ratio for stiffened TCSPSWs is proposed and illustrated with several calculation examples. According to the above analyses, the relationship between the rigidity ratio and elastic buckling coefficient for the stiffened TCSPSWs can be further established, and procedures to calculate the elastic coefficient for stiffened TCSPSWs at the global buckling stage are proposed. Finally, finite element (FE) model is developed to validate the theoretical model, based on which parametric studies are conducted to explore the influences of several design parameters on elastic buckling, including ratio of rigidity constants, width-to-height ratio, and thickness of the trapezoidal corrugated steel plate, etc. Results show that the proposed theoretical solution can be applied to describe the elastic buckling behavior of stiffened TCSPSWs with enough accuracy in practical design.

Numerical study on contact force of paralleled beveloid gears using minimum potential energy theory

Using minimum potential energy theory and slicing method, a computational approach to calculate the magnitude and distribution of contact force for paralleled beveloid gear pair was proposed in this article. The theoretical tooth contact model was built based on spatial gearing theory to calculate the mesh parameters including the coordinates, normal vectors, and equivalent radius for meshing points. Then, the analytical contact force model of paralleled beveloid gear pair was derived based on minimum potential energy theory. Finite element contact analysis was conducted to verify the proposed model. Finally, the influences of macro-geometry design parameters on the contact force distribution were investigated. Results show that the pressure angle has a limited influence on the contact force distribution. The increase in helix and cone angles will observably increase the asymmetry of contact force distribution as well as the fluctuation of contact force distribution for a single tooth. A good correlation was obtained between the proposed analytical model and the finite element model for the distribution and magnitudes of contact force.

Numerical simulation of flow patterns and the effect on heat flux during R32 condensation in microtube

Based on the fluid volume approach, a transient numerical model for the condensation heat transfer and flow features in a microchannel is proposed. The flow condensation of R32 in a circular microtube with 0.1 mm diameter was studied. Four typical flow patterns, annular, injection flow, slug flow and bubbly flow are simulated along a two-dimension calculational domain successively. The numerical mode is verified by the experiments from the literature. The numerical results discern that the increase of mass flux, wall temperature and saturation temperature affect the detachment point of vapor slug further toward the outlet with higher occurrence frequency, which can be attributed to the higher Weber number and Capillary number of tail vapor core respectively. The local heat flux and wall shear stress will decrease along the flow direction overall, and tend to be constant in the single phase liquid area. However, there exit some rebounds and oscillations of the local heat flux and wall shear stress during injection and slug flow. The transient oscillations of wall shear stress can induce fluctuations and even waves in the annular flow upstream, which can be concluded as “surface tension force affecting upstream”, is proposed based on the minimum potential energy theory. This mechanism could be a supplement for the traditional theory of “flow pattern transition at high mass flux being induced by fluctuations which grow up while flowing downstream”.

Long-term stability analysis of goaf area in longwall mining using minimum potential energy theory

Estimation of the height of caved and fractured zones above a longwall panel along with the stability conditions of the goaf area are very crucial to determine the abutment stresses, ground subsidence, and face support as well as designing the surrounding gates and intervening pillars. In this work, the height of caving-fracturing zone above the mined panel is considered as the height of destressed zone (HDZ). The long-term estimation of this height plays a key role in the accurate determination of maximum ground surface subsidence and the amount of transferred loads towards the neighbouring solid sections. This paper presents a new stability analysis model of caved material system in the goaf area. For this aim, a theoretical energy-based model of HDZ determination in long-term condition is developed. Then the stability condition of the caved material system is investigated using the principle of minimum potential energy. On the basis of the actual data gathered from the literature, the unstable time period of the caved material system is also calculated. Moreover, the effects of time- and temperature-related parameters and constant coefficients as well as their inherent relations with HDZ are evaluated. Furthermore, sensitivity analysis shows that the two temperature-related constants material constant and time are the most effective variables in HDZ, and the slope of material hardening is the least effective one. The estimated HDZ and the stability time of the caved materials can be successfully applied to determine the induced stress and the maximum surface subsidence, respectively, due to longwall mining.

Helical buckling of a thin rod with connectors constrained in a torus

Kinds of tubular strings are widely applied to oil exploration & development. In the preceding studies, theses tubular strings are usually taken as homogeneous thin rods without connectors constrained in a straight cylinder or torus. Recent studies have indicated that the effect of connectors on the tubular strings is ignorable. On the basis of the previous studies, the paper provides an analytical model describing the helical buckling behaviors of a rod with connectors constrained in a torus. The new model is solved based on beam-column model and minimum potential energy theory. There are three contact cases between the rod and the torus, namely no contact, point contact and wrap contact. The deflections of the rod and critical conditions between different contact cases are calculated. The results show that the deflections and critical conditions are quite different when the equivalent torus curvature radius changes. The effects of equivalent torus curvature radius, rod buckling and connectors on bending moment and contact force are analyzed. The results show that connector is an important factor which should not be neglected.

Elastic buckling of cylindrical pipe linings with variable thickness encased in rigid host pipes

Cured-in-place plastic pipe linings are widely used in the rehabilitation of deteriorated rigid pipelines. Generally, the thickness of the pipe lining is assumed to be constant for simplification during the previous analysis. However, the thickness of the pipe lining may be a variable due to corrosive liquids or gases in service. This paper develops an analytical solution for the elastic buckling of cylindrical pipe linings with variable thickness subjected to external hydrostatic pressure. In addition to the analytical solution based on the minimum potential energy theory, a numerical analysis using the finite element method (FEM) is also performed for comparison. The FEM results agree well with the analytical solutions. Both the FEM results and the analytical solutions are discussed and compared with the models presented by other authors. When the thickness of pipe lining is constant, our analytical solutions can be simplified to Glock's typical solutions.

Elastic Stability Analysis of a Two-Layered Functionally Graded Cylindrical Shell under Axial Compression with the use of Energy Approach

This paper investigates the elastic axisymmetric buckling of a thin, simply supported functionally graded (FG) cylindrical shell embedded with an elastic layer under axial compression. The analysis is based on energy method and simplified nonlinear strain-displacement relations for axial compression. Material properties of functionally graded cylindrical shell are considered graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Using minimum potential energy together with Euler equations, equilibrium equations are obtained. Consequently, stability equation of functionally graded cylindrical shell with an elastic layer is acquired by means of minimum potential energy theory and Trefftz criteria. Another analysis is made using the equivalent properties of FG material. Numerical results for stainless steel-ceramic cylindrical shell and aluminum layer are obtained and critical load curves are analyzed for a cylindrical shell with an elastic layer. A comparison is made to the results in the literature. The results show that the elastic stability of functionally graded cylindrical shell with an elastic layer is dependent on the material composition and FGM index factor, and the shell geometry parameters and it is concluded that the application of an elastic layer increases elastic stability and significantly reduces the weight of cylindrical shells.

Finite element analysis of conical, dome and truncated InAs quantum dots with consideration of surface effects

Surface effects on conical, dome and truncated InAs quantum dots (QDs) grown on GaAs (0 0 1) substrate are quantitatively analyzed with the finite element method (FEM) taking into account the surface energy. It is found that surface effects hinder island formation and arouse changes in strain fields of QDs. According to the minimum potential energy theory, the shape transition from conical island to dome island at a certain critical point is interpreted. We conclude that conical QD or truncated QD are transitional shapes at early stages while dome QD is the mature shape in this case.

Investigating elastic stability of cylindrical shell with an elastic core under axial compression by energy method

In this paper, the elastic axisymmetric buckling of a thin, isotropic and simply supported cylindrical shell with an elastic core under axial compression has been analyzed using energy method. The nonlinear strain-displacement relations in general cylindrical coordinates are simplified using Sanders kinematic relations (Sanders, 1963) for axial compression. Equilibrium equations are obtained by using minimum potential energy together with Euler equations applied for potential energy function in cylindrical shell. To acquire stability equation of cylindrical shell with an elastic core, minimum potential energy theory and Trefftz criteria are implemented. Stability and compatibility equations for an imperfect cylindrical shell with an elastic core are also obtained by the energy method, and the buckling analysis of shell is carried out using Galerkin method. Critical load curves versus the aspect ratio are obtained and analyzed for a cylindrical shell with an elastic core. It is concluded that the application of an elastic core increases elastic stability and significantly reduces the weight of cylindrical shells.

Measurement of Mechanical Properties and Residual Stresses of Bridged Gold Films and Circular Gold Membranes

In order to measure the mechanical properties of gold films on silicon substrate, two types of specimens, i.e., bridged films and circular membranes, are manufactured. Using a wedge tip, the bridged gold films are indented so that the films are pushed off, which is called as V-peel test. The load-deflection curves obtained by the V-peel test are analyzed with the concept of geometrically nonlinear beam by using the minimum potential energy theory together with Ritz method. Thus, Young’s modulus and residual stress of the bridged gold films are obtained. Blister test is also conducted to measure the Young’s modulus and residual stress of a circular gold membrane, of which deformation is measured by Twyman-Green interferometer. By gradually increasing the external pressure applied on the membrane, the interfacial fracture toughness between the gold membrane and silicon substrate is measured based on the concepts of interfacial fracture mechanics.

Modeling Machining Geometric Variation in a N-2-1 Fixturing Scheme

Fixtures are used to locate and constrain workpieces in machining. Fixture properties, such as accuracy and locator layout schemes, directly affect the resultant geometric variation on the machined workpiece surfaces. N-2-1 fixturing schemes (N>3) are often used for large or compliant workpieces in machining. However, the impact of N-2-1 fixturing on product geometric variation is not well understood because of the uncertainty of contact under the overconstraint condition. This paper presents a modeling methodology to study the machining geometric variation in a 4-2-1 fixturing scheme. The model integrates the fixture-workpiece interactions resulted from the rigid-body variation in fixtures, workpieces, and machine tools, and the static deformation under external forces. The uncertainty of the fixture-workpiece contact condition due to the 4-2-1 constraint condition is modeled using the minimum potential energy theory. A numerical example of face milling is presented to demonstrate the methodology.