Potential Energy Criterion Research Articles

A two-stage parallel hybrid method for power system dynamic security assessment

Abstract The present paper introduces a hybrid method based on both the Lyapunov’s direct approach using the Potential Energy Boundary Surface method and parallel time-domain simulation for fast power system dynamic security assessment. The main contribution in the presented method is an approach that combines the directional derivative of the potential energy function and the maximum potential energy criterion in order to reduce the conservativeness in the estimation of the stability region at the direct method stage. For detailed investigation of the critical contingencies, a parallel approach is applied at the time-domain simulation stage. From the simulation results, the proposed method achieves a high level of accuracy in classifying network contingencies and shows great computational performance potential in light of the requirement for fast dynamic security assessment.

The computational study of crack growth process in defected polymethyl methacrylate/hydroxyapatite composite beam: peridynamic simulation

The presence of cracks in structural materials can be attributed to a wide array of factors. Gaining a comprehensive understanding of the underlying influences on crack formation in solid structures holds significant implications for the development of efficient industrial equipment. In the present computational investigation, we employ the peridynamic method to characterize the crack growth process in polymethyl methacrylate/hydroxyapatite beams. This particle-based simulation encompasses two fundamental steps. Initially, a modeled composite is brought to equilibrium under standard conditions, followed by an in-depth analysis of the crack growth phenomenon after subjecting the target structure to impact tests at three distinct velocities. The present investigation aims to quantitatively assess a range of physical parameters, such as crack length, repulsive force, relative bond length, potential energy, and damage criterion, to provide a comprehensive characterization of the crack growth process in polymethyl methacrylate/hydroxyapatite-based samples. The computational tool utilized for conducting the peridynamic simulations is the Large Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The findings from the peridynamic analysis demonstrate a clear association between the ratio of hydroxyapatite and the resulting crack length in the sample, which consequently leads to heightened brittleness and a decrease in mechanical strength. The crack length ratio reaches a measurement of 9.09 mm when the beam under consideration contains 15% hydroxyapatite. The observed behavior can be ascribed to a reduction in the attractive forces acting between the constituent particles present in the sample. The numerical findings derived from this investigation possess significant implications for the development of mechanically robust composites in practical contexts.

An investigation of aero-thermo-elastic flutter and divergence of functionally graded porous skew plates

Aero-thermo-elastic flutter and divergence analyses of functionally graded (FG) porous skew plates subjected to supersonic airflow are investigated in this study. The material properties of skew plates vary across the thickness based on the modified power-law model. Three types of thermal loading as constant, linear and nonlinear temperature distributions in the thickness direction of the plate are considered. Applying the Hamilton’s principle, the coupled partial differential equations of motion and the associated boundary conditions based on the first-order shear deformation theory and linear piston theory are derived in the Cartesian coordinates. Also, the principle of minimum total potential energy and adjacent equilibrium criterion are used to obtain the stability equations. Using a mapping, the partial differential equations of motion and stability equations are converted from Cartesian coordinate system to a skew coordinate. The partial differential equations in the skew coordinate are discretized by generalized differential quadrature method (GDQM) and solved using the state space method. Consequently, the effects of geometrical, mechanical and thermal parameters such as thermal loading types, angle of skew, power-law index, porosity, and boundary conditions on the flutter and divergence boundaries of skew plate are studied in detail.

Out-of-Step detection based on an improved line potential energy criterion

The line potential energy in the cutset is used as the criterion for monitoring the generator instability, but the criterion has the following two limitations due to narrowly defined conditions. The assumption of an ideal constant power load is difficult to satisfy, and the condition of the critical cutset is too narrow. The limitations are addressed by analyzing the relationship between the power of the load elements and the power of the cutset based on the two-machine equivalent. Modifications of the theoretical derivation steps of this criterion are presented to extend the applications of the criterion and provide theoretical support for its online use. Two simple strategies are proposed to ensure early detection of the generator instability.

Progressive Failure Analysis of Thin-Walled Composite Structures Verified Experimentally.

The subject of the presented research was a thin-walled composite column made of CFRP (carbon-epoxy laminate). The test sample had a top-hat cross-section with a symmetrical arrangement of laminate layers [90/−45/45/0]s. The composite structure was subjected to the process of axial compression. Experimental and numerical tests for the loss of stability and load-carrying capacity of the composite construction were carried out. The numerical buckling analysis was carried out based on the minimum potential energy criterion (based on the solution of an eigenvalue problem). The study of loss of load-carrying capacity was performed on the basis of a progressive failure analysis, solving the problem of non-linear stability based on Newton-Raphson’s incremental iterative method. Numerical results of critical and post-critical state were confronted with experimental research in order to estimate the vulnerable areas of the structure, showing areas prone to damage of the material.

Stability Analysis of Composite Columns under Eccentric Load

Short thin-walled CFRP columns with channel section were investigated in this study. The tested columns were subjected to compressive load, both axial and eccentric. Eccentric load was applied in two mutually perpendicular directions. The scope of the study included examining the effect of load eccentricity on the critical load of the column. The study involved both experimental tests performed on physical models of columns created by the autoclave technique and a numerical analysis by the finite element method. The numerical analysis of critical state involved solving an eigen problem by the minimum potential energy criterion in order to determine the buckling mode and a corresponding critical load. For physical models, the critical load was determined based on tensometric measurements by Koiter’s approximation method. The numerical results were compared with experimental findings. The study determined the effect of eccentric compressive load on the critical load of the tested column and that of composite lay-up on the structure’s stability.

Symmetric snap-through and equal potential energy load of non-uniform shallow arch under a concentrated load considering imperfection effect

This paper deals with analytical investigation of non-uniform circular shallow arch under a concentrated load considering imperfection effect under pinned-pinned boundary conditions. After characterizing the non-uniformity by three piecewise constant stiffness segments, governing equilibrium equations including imperfection effect are derived via least potential energy principle and criteria for possible occurrence of symmetric snap-through are explicitly presented by using L'Hospital's rule after identifying two modified slenderness parameters. The existence of an equal potential energy load is rigorously shown in a straightforward manner and its parametric dependence on imperfection and non-uniformity is discussed. The relationship between equal potential energy load and buckle propagation load is studied by 3D FEA of buckle propagation of corresponding non-uniform shallow panel. Moreover, two limiting cases including rigid end case and rigid center case are analyzed by employing augmented potential energy with Lagrangian multipliers. An asymptotical solution shows that a finite modified slenderness (independent of imperfection) is sufficient to ensure the occurrence of symmetric snap-through when dimension of center segment is approaching to zero in rigid end case and this conclusion holds when there is some rotational restraint at ends. For rigid center case, the closed-form criterion considering imperfection for symmetric snap-through occurrence is presented. Equal potential energy load for two limiting cases is derived and analyzed in detail. This paper is expected to enhance the understanding of stability of imperfect non-uniform shallow arch.

Linear stability and energetics of rotating radial horizontal convection

The effect of rotation on horizontal convection in a cylindrical enclosure is investigated numerically. The thermal forcing is applied radially on the bottom boundary from the coincident axes of rotation and geometric symmetry of the enclosure. First, a spectral element method is used to obtain axisymmetric basic flow solutions to the time-dependent incompressible Navier–Stokes equations coupled via a Boussinesq approximation to a thermal transport equation for temperature. Solutions are obtained primarily at Rayleigh number $\mathit{Ra}=10^{9}$ and rotation parameters up to $Q=60$ (where $Q$ is a non-dimensional ratio between thermal boundary layer thickness and Ekman layer depth) at a fixed Prandtl number $\mathit{Pr}=6.14$ representative of water and enclosure height-to-radius ratio $H/R=0.4$. The axisymmetric solutions are consistently steady state at these parameters, and transition from a regime unaffected by rotation to an intermediate regime occurs at $Q\approx 1$ in which variation in thermal boundary layer thickness and Nusselt number are shown to be governed by a scaling proposed by Stern (1975, Ocean Circulation Physics. Academic). In this regime an increase in $Q$ sees the flow accumulate available potential energy and more strongly satisfy an inviscid change in potential energy criterion for baroclinic instability. At the strongest $Q$ the flow is dominated by rotation, accumulation of available potential energy ceases and horizontal convection is suppressed. A linear stability analysis reveals several instability mode branches, with dominant wavenumbers typically scaling with $Q$. Analysis of contributing terms of an azimuthally averaged perturbation kinetic energy equation applied to instability eigenmodes reveals that energy production by shear in the axisymmetric mean flow is negligible relative to that produced by conversion of available potential energy from the mean flow. An evolution equation for the quantity that facilitates this exchange, the vertical advective buoyancy flux, reveals that a baroclinic instability mechanism dominates over $5\lesssim Q\lesssim 30$, whereas stronger and weaker rotations are destabilised by vertical thermal gradients in the mean flow.

Generating human-like movements for robotic arms

In this paper, the generation of trajectories of both end-effector and joints for human-like reaching and grasping motions is studied. In reaching movement, the human-like end-effector trajectory is obtained based on the minimum jerk model. A total potential energy criterion is constructed to resolve the kinematic redundancy of human arm in the target position. Gradient Projection Method (GPM) is adopted to trace the human-like end-effector trajectory while minimizing the total potential energy to generate the human-like joint trajectory. In grasping movement, the total potential energy and wrist discomfort are synthesized to resolve the kinematic redundancy of human arm in the target position and orientation. A new planner, Gradient Projection Method based Rapidly-exploring Random Tree (GPM-RRT) algorithm, is proposed to generate the human-like end-effector trajectory by goal biasing and the human-like joint trajectory by minimizing the synthesis of the total potential energy and wrist discomfort. The criteria and algorithm are verified by simulations and experiments.

A Levy-type solution for buckling analysis of micro-plates considering the small length scale

In this paper, a Levy-type solution based on the modified couple stress theory is developed to study the buckling behaviors of micro-plates. Based on this theory, length scale parameter is considered to capture the size effect of rectangular micro-plates. Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain the stability equations and corresponding boundary conditions. Different boundary conditions with two opposite edges simply supported and arbitrary boundary conditions along the other edges are considered. To illustrate the new model, both uniaxial and biaxial loads are applied and the critical buckling loads are defined for over a wide range of thickness, different length scale parameters and various boundary conditions. To show the accuracy of the formulations, present results are compared with available results in literature for specific cases and a very good agreement is observed. Results reveal that the critical buckling load increases as the length scale parameter increases especially when the thickness of the micro-plates becomes in order of length scale parameter and this effect is more significant for free boundary condition.

Three-Dimensional Dynamic Analysis on Soil-Structure Applying Mixed Linear-Nonlinear Substructure Method

To increase the computation efficiency of the three-dimensional nonlinear dynamic analysis of soil-structure, the liner-nonlinear mixed constrained mode synthesis method was put forward according to the characteristic that the structure owns local plastic region, which is appropriate for both nonlinear substructure and multi linear substructures with boundary coupling. Divided the whole system into linear substructure and nonlinear substructure, this method reduced the freedom degree of linear substructure according to the potential energy criterion and finally synthesized them with the nonlinear substructure, thus obtaining the dynamic response of nonlinear system. The accuracy and effectiveness of this method were proved by further applying this method in the three-dimensional dynamic analysis example of soil-high building interaction system to carry out dynamic time-history analyses under the effect of multi-groups earthquake incentives respectively for two different boundary conditions of soil mass. Finally, several groups of numerical experimentations were conducted based on the various different values of nonlinear soil mass region, and the result indicated that as far as the example of this paper was concerned, it can obtain satisfiable computation result when the range of nonlinear soil mass region was 3 times of the horizontal size of upper structure, which further demonstrated the effectiveness of the method proposed in this paper.

Linear thermal buckling analysis of truncated hybrid FGM conical shells

In this study buckling analysis of a functionally graded conical shell integrated with piezoelectric layers that is subjected to combined action of thermal and electrical loads is presented. The material properties of functionally graded conical shells are assumed to vary continuously through the thickness direction based on a power law form. The governing equations, including the equilibrium and stability equations, are obtained based on the classical shell theory and the Sanders nonlinear kinematics relations. The case of uniform temperature distribution through the shell domain is considered. The prebuckling forces are obtained considering the membrane solutions of linear equilibrium equations. Minimum potential energy criterion is employed to establish the stability equations. The single-mode Galerkin method is used to obtain the critical buckling temperature difference. The results are compared with the known data in the open literature. Finally, some numerical results are presented to study the effects of applied actuator voltage, shell geometry, and power law index of FGM on thermal buckling behavior of the conical shell.

扩展有限元法在准脆性混凝土结构断裂中的数值模拟

扩展有限元法是基于自适应离散裂纹方法进行的混凝土裂纹扩展仿真模拟。并采用接触边界模型，接触边界模型包括正向位移和切向位移，允许通过界面进行剪切应力的传递，在扩展有限元法的框架中，对一个有凝聚力的裂纹扩展的延伸方向的研究有不同准则。通过两个例子，对最大周向应力理论，最大能量释放率理论和最小势能理论的实验数据进行了比较并形成规范。采用XFEM方法在一般加载模式I型和混合型加载条件下进行的混凝土断裂扩展数值模拟的灵活性和有效性已经得到了证实。 In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Analysis of Lubricating Performance for Involute Gear Based on Dynamic Loading Theory

An integrated model for gear pair that combines the dynamic load with the mixed elastohydrodynamic lubrication (EHL) theory is proposed in this paper covering the film squeeze effect as well as the friction force generated from the rough surfaces. Comparisons between the two models of load which are, respectively, based on minimum elastic potential energy (MEPE) criterion and dynamic motion equations built up in this paper are discussed. The results show that at low speed the loads calculated by the two models are similar. However, with increasing speed, the load exhibits dynamic characteristics gradually and reaches the highest value at resonant speed. Besides, the effects of the helix angle and the lubricant viscosity are also analyzed. Increasing the ambient viscosity could intensify the film stiffness and viscous damping. Gear with larger helix angle could weaken the impact phenomenon at the shift points where one tooth-pair disengages. Moreover, it is symmetric with regard to the pressure and film thickness across the face width for spur gear. Differently, the pressure for helical gear has a higher value at the dedendum of pinion where the film becomes thinner. In addition, speeding up the pinion would generally result in higher dynamic load and film pressure but thicker film thickness.

Numerical Simulation of Quasi-Brittle Fracture in Concrete Structures with Extended Finite Element Method

In this paper, the extended finite element method (XFEM) is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm. An interface model is proposed which includes normal and tangential displacements and allows the transfer of shear stresses through the interface. Different criteria for predicting the direction of the extension of a cohesive crack are conducted in the framework of the XFEM. On the basis of two examples, a comparison between the maximum circumferential stress criterion, the maximum energy release rate and the minimum potential energy criterion with experimental data has been carried out. The considered numerical simulations have confirmed the flexibility and effectiveness of the XFEM for the modelling of crack growth under general mode I and mixed-mode loading conditions.

Configuration energy analysis of β-Mg2Al3 cluster structure

Stability of (Mg-Al) clusters in the β-Mg2Al3 structure has been studied with the use of the effective pair potential of interatomic interactions taken from ab-initio calculations. The total potential energy has been calculated for various possible (Mg-Al) cluster configurations in order to find the optimal ones. The computation has been started from the cluster located at the 8(b) site consisting of 72 partially occupied, overlapping atomic sites, as determined by X-ray studies. The configurations of fully occupied, non-overlaping atomic positions have been selected using the criterion of minimal potential energy. The simulated annealing algorithm has been used for further optimization of the atomic positions in 3D space. The energy optimization leads to the selection of several configurations with the energy close to the minimum. For such structures the configuration entropy has been calculated as a function of the total potential energy. More complex structures, consisting of the optimized clusters and various interface configurations, have been also studied.

Nonclassical Linearization Criteria in Nonlinear Stochastic Dynamics

Abstract In classical stochastic linearization method, the nonlinear force is replaced by an equivalent linear one. Several nonclassical schemes were suggested in recent years, based on potential or complementary energy criteria. Here, these criteria are compared with each other, and the classical stochastic linearization scheme, to determine their efficacy.

Load distribution model along the line of contact for involute external gears

Abstract Calculation methods of spur and helical gears for preliminary designs or standardization purposes available in technical literature use simple equations given by the linear theory of elasticity (Navier’s equation) and the Hertzian contact model to evaluate the bending and contact stresses, assuming the load to be uniformly distributed along the line of contact. However, these models are not in good agreement with experimental results because the changing meshing stiffness of the pair of teeth along the line of action produces a non-uniform load distribution, causing some load distribution factors to be required to compute bending and contact stresses. In this paper, a model of non-uniform load distribution along the line of contact, obtained from the minimum elastic potential energy criterion, is presented. This model combined with the equations of Navier and Hertz yields more realistic values of the bending and contact stresses. An approximate, accurate equation for the inverse unitary potential, allowing analytic calculations of the load per unit of length at any point of the line of contact and any position of the cycle of meshing, is also presented. The same equation, with a slight modification of the coefficients, is also valid for undercut teeth. Results have been validated by comparison with some studies carried out by the Finite Element Method.

Sensitivity of ITCZ configuration to cumulus convective parameterizations on an aqua planet

This paper examines the performances of various cumulus convective parameterization schemes in the tropical atmosphere using an aqua-planet atmospheric General Circulation Model forced by zonally symmetric but latitudinally varying sea surface temperature (SST) and solar angle. The intertropical convergence zone (ITCZ) is represented by intense precipitation. The assigned Control experiment with a specific SST distribution, as designated by the Aqua Planet Experiment, yields a single ITCZ when Zhang’s scheme or Manabe’s scheme is employed, whereas a double ITCZ occurs when Tiedtke’s scheme is used. The key to the occurrence of a double ITCZ is latitudinal variation in evaporation within the boundary layer. Such variation is induced mainly by latitudinal variation in the zonal wind speed, with the existence of a calm belt at the equator and a maximum wind speed located off the equator, arising from the evaporation–wind feedback (EWF) mechanism. The latitudinal distribution of evaporation results in a decrease in the height of the lifting condensation level in areas off the equator and an increase at the equator. The occurrence of a single ITCZ in Zhang’s scheme is attributed to the use of a Convective Available Potential Energy criterion by which convection occurs more readily at the equator. As a result, a precipitation maximum is maintained at the equator via a prevailing Conditional Instability of the Second Kind mechanism.

Mechanical properties of ferrofluid applications: Centering effect and capacity of a seal

This paper presents three-dimensional study of a ferrofluid seal, its centering effect and its static capacity. Thus, a method based on a potential energy criterion has been put forward to study the seal shape. But such a use of ferrofluid seals is interesting only if the magnetic field created by the permanent magnets saturates totally the ferrofluid. Two cylindrical structures consisting of two and three outer ring permanent magnets with an inner non-magnetic cylinder are considered. The calculation of the magnetic pressure of the ferrofluid seal is analytically established.