Minimum Potential Energy Research Articles

Broad-range high-resolution optical spectroscopy of CH3NH3PbBr3 hybrid perovskite single crystals: Optical phonons, absorption edge, phase transitions

Vibrational and structural properties have an enormous influence on optoelectronic properties of hybrid halide perovskites CH3NH3PbX3 (X = I, Br, Cl), which are perspective materials for different photovoltaic applications. Here, we report results of the first high-resolution optical spectroscopy measurements of large CH3NH3PbBr3 single crystals in wide frequency (20–20 000 cm−1) and temperature (5–300 K) ranges. Fit of polarized far-infrared reflection spectra using Lorentz model of damped oscillators revealed parameters of three phonons at room temperature and 38 phonons at 10 K. An analysis of mid-infrared transmission spectra gave evidence of a strong anharmonicity in this hybrid perovskite. A splitting of some lines observed in the orthorhombic phase was presumably assigned to the tunneling of the CH3NH3+ cation molecule between several potential energy minima. The temperature behavior of the transmission spectra near the fundamental absorption edge was tentatively explained by the competition between two different exciton transitions in CH3NH3PbBr3. Positions of spectral lines and of the absorption edge measured at cooling and heating the sample demonstrate hysteresis loops in the vicinities of phase transitions around 237, 155, and 149 K, thus revealing the first-order nature of all three phase transitions in CH3NH3PbBr3.

Cross-section geometry optimization of flexural thread using energy criterion

Purpose: The aim of this work is to develop a method to determine the best geometrical parameters of the flexural thread cross-section providing the lowest potential energy of deformation, thereby meeting the requirements for the minimum weight based on strength and rigidity limitations on the designed element.Methodology/approach: The problem of calculating the best parameters is reduced to nonlinear mathematical programming using the energy criterion. The latter provides to gain the minimum potential energy of deformation of the designed element.Research findings: The proposed methodology allows evaluating the results obtained. The numerical experiment determines the optimum cross-section geometry of flexural thread. The spread in values between proposed methodology and finite element method are insignificant.Practical implications: The proposed method provides the solution of inverse problems in a geometrically nonlinear formulation, including a search for optimum geometrical parameters of elements that combine the operation of beams and flexural thread. The proposed method can be used at the design stage of large-span shells of buildings.

Buckling responses and instability mode landscapes of composite sandwich panels with extreme auxeticity based on higher-order shear and normal deformation theory

Sandwich structures have been a subject of intense scrutiny and utilization in engineering applications. However, there has been a limited understanding of the mechanical behaviors of novel sandwich structures composed of auxetic metamaterials. This study aims to contribute to the body of knowledge by examining the buckling responses of sandwich beams or wide plates with an orthotropic anti-tetra chiral lattice (ATCL) aluminum cores and symmetric angle-ply carbon-fiber/epoxy face sheets, both of which can exhibit highly negative Poisson’s ratios or extreme auxeticity. The linear stability analysis of the sandwich structures under axial compression is conducted by applying the minimum potential energy principle and solving the eigenvalue problem using a numerical method. To achieve an accurate representation of arbitrary two-dimensional buckling morphologies, the first- and fifth-order shear and normal deformation models are employed to simulate the transverse kinematics of the face sheets and cores, while the finite-element model is utilized to discretize the longitudinal displacement of all constituents. The investigation reveals new insights into the interrelationship between global buckling, facial wrinkling, and shear crimping in conventional sandwich structures. The effects of material auxeticity on buckling responses are analyzed across an extensive range of geometrical configurations for the first time, unveiling five unprecedented buckling mode shapes, sophisticated buckling mode landscapes, and Poisson’s ratio-sensitive buckling criteria. These findings lay a crucial foundation for designing and optimizing auxetic sandwich structures, bringing diverse possibilities in lightweight constructions, acoustic insulation, energy absorption, and dynamic and shock mitigation.

Structural optimization of an encased bi-material FGP-GNF pipeline-liner system with novel polyhedral configurations

This article proposes a novel thin-walled polyhedral functionally graded porous (FGP) liner consolidated by graphene nanofillers (GNF) to rehabilitate the cracked pipeline. A buckle propagation may occur since the liner is subjected to hydrostatic pressure and temperature variational field simultaneously. A cosine function is developed to describe the deformed shape of the liner. Both pores and the GNF are distributed symmetrically on the cross-section of the liner, which also has a polyhedral profile to improve its bending stiffness. The nonlinear equilibrium equations are accurately obtained by introducing the thin-walled shell theory and the principle of minimum potential energy. The critical buckling pressure is obtained by solving the nonlinear equilibrium equations. Analytical solutions are compared successfully with other closed-form results to accomplish the verification when the FGP-GNF polyhedral liner reduces to an isotropic circular one. Furthermore, one improvement factor is proposed to analyze the effect of different polyhedral shapes on the buckling pressure of the encased polyhedral FGP-GNF liner. Finally, parameters are evaluated to further understand the buckling behavior of the FGP-GNF polyhedral liner, including the number of polygons, porosity coefficient, mass fraction, geometric shape of the GNF, radius-to-thickness ratio, temperature field, etc.

Influence of surface effect on post-buckling behavior of piezoelectric nanobeams

Piezoelectric nanobeams with excellent mechanical, thermal and electrical properties are important components in micro-nano electromechanical systems, which are widely used as sensors, brakes and resonators. Based on the Euler–Bernoulli beam model, the influence of surface effect on the post-buckling behaviour of piezoelectric nanobeams is analysed. According to the surface elasticity theory and the ‘core–shell’ model, the surface energy model is used to introduce the influence of surface effect. The governing equations and boundary conditions of the post-buckling of piezoelectric nanobeams under the influence of surface effect are derived by the principle of minimum potential energy. The analytical solution of post-buckling is obtained by the eigenvalue method. The influence of surface effect on the post-buckling configuration, post-buckling path, amount of induced charge and critical load of piezoelectric nanobeams with different external constraints and cross-sectional dimensions are discussed. The results show that surface effect has a significant influence on the post-buckling of piezoelectric nanobeams. Considering surface effect, the effective elastic modulus and critical load of piezoelectric nanobeams are increased, and the post-buckling configuration, post-buckling path and amount of induced charge are reduced. These findings contribute to the study of micro-nano electromechanical systems based on nanobeam structures and provide a theoretical basis for the design and manufacture of nanodevices.

Static and dynamic nonlinear behavior of a multistable structural system consisting of two coupled von Mises trusses

Recent years have witnessed a growing interest in multistable structures. In most cases it is attained by a sequence of bistable elements. However, little is known on their nonlinear static and dynamic responses. In this work a detailed static and dynamic nonlinear analysis of a multistable structural system consisting of two coupled bistable von Mises trusses is conducted to enlighten the complex behavior of these systems. For this, the exact nonlinear equilibrium equations and equations of motion in their dimensionless forms are obtained through the principle of stationary potential energy and Hamilton’s principle, respectively, considering a linear elastic material. Using continuation algorithms, the nonlinear equilibrium paths are obtained. The stability of each configuration is analyzed using the principle of minimum potential energy. Multiple equilibrium paths of the coupled system are identified, leading to several coexisting stable and unstable solutions, bifurcations and potential wells which are closely connected to the symmetries of the system. It is shown that the number of coexisting solutions increases exponentially with the number of bistable units. The effect of unavoidable imperfections is also clarified. The nonlinear dynamics and bifurcations of the system under harmonic forcing and static pre-load are then studied. Bifurcation diagrams, Poincaré maps and cross-sections of the basins of attraction are used to study the influence of coexisting attractors due to multiple potential wells, resonances and bifurcations. The coexisting responses can merge giving rise to several types of cross-well motions, the threshold value being closely connected with the limit point load of the coupled system. The increase in coexisting solutions leads to increasingly complex basins of attraction with broad fractal regions. On the one hand, the complexity of the bifurcation scenarios seems valuable in several applications to encode information, to respond to external forcing and to switch between different states. On the other hand, multiple attractors and their fractal basins can lead to the loss of global stability and dynamic integrity due to the small uncorrupted basins surrounding each attractor. Thus, the knowledge of the static and dynamic behavior of multistable systems is of great significance to either inducing or avoiding this phenomenon or making use of it.

Buckling of a movable constrained laminated beam with variable-length in hygrothermal environment

The buckling response of a variable-length laminated beam constrained by a pair of symmetrical walls in hygrothermal environment is studied in the paper. The constrained wall is rigid but supported by springs that move upwards as a whole after being subjected to a force. The nonlinearly constrained buckling governing equation of the variable-length laminated beam in hygrothermal environment is established based on the principle of minimum potential energy and the Lagrange multiplier method. The buckling responses of the variable-length laminated beam are derived based on the elliptic integral method. Extensive numerical calculations are performed to illustrate the effects of different constraint clearances, spring stiffness, geometry, temperature, humidity, and composite fiber ply angle on the critical buckling load, buckling response, and buckling path.

A Moving Kriging Interpolation Meshless for Bending and Free Vibration Analysis of the Stiffened FGM Plates in Thermal Environment

This paper adopts the Moving Kriging (MK) interpolation meshless method to analyze the static and dynamic behaviors of stiffened functionally graded material (FGM) plate in thermal environment based on the physical neutral surface. The ribbed FGM plate is regarded as a composite structure of a FGM plate and ribs. The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and MK interpolation. The meshfree model for ribbed FGM plate is obtained by superimposing the total energy of the FGM plate and the stiffeners based on the first-order shear deformation theory (FSDT) and physical neutral surface. The nonlinear temperature field along thickness direction is introduced into the meshless model of stiffened FGM plate. The equations governing the bending and free vibration of the ribbed FGM plate in thermal environment are obtained according to the principle of Minimum Potential Energy and Hamilton’s Principle. Thereafter, several ribbed FGM plate examples in different temperatures and with different locations of ribs are calculated. The results are compared with those given by the ABAQUS and literature. The results show that the effectiveness and accuracy of the proposed method in analyzing the ribbed FGM plate in thermal environment.

Nonlinear Stress-Free-State Forward Analysis Method of Long-Span Cable-Stayed Bridges Constructed in Stages

Structural analysis and construction control of staged-construction processes are major subjects in the context of modern long-span bridges. Although the forward and backward analysis methods are able to simulate situations, their main disadvantage is that they usually apply the stage superposition principle. In the actual construction process, due to changes made to the plan, the construction process needs to be adjusted at any time, and it is difficult to implement the construction process in complete accordance with the established plan. As a result, the existing simulation method based on the incremental structural analysis of each construction stage has poor adaptability to such adjustments. In this study, considering the strong geometric nonlinear behavior of the long-span cable-stayed bridge construction process, the geometrically nonlinear mechanical equations of the staged-construction bar system structure were derived. The minimum potential energy theorem was used by introducing the concept of the stress-free-state variable of the structural elements. The equation reflects the influence of the change in the stress-free-state variables of structural elements on the completion state of the structure. From the analysis of the geometrical condition that the equilibrium equation holds, the stress-free installation condition of the closing section of the planar beam element structure was obtained. A new simulation method for long-span cable-stayed bridge construction has been proposed, which is called the stress-free-state forward analysis. This method can directly obtain the intermediate process state of cable-stayed bridge construction without performing stage-by-stage demolition calculations, and causing the internal force and deformation of the completion state to reach the design target state. This method can realize the simulation of multi-process parallel operation in construction, and solves the problem of automatic filtering of temporary loads. To illustrate the application of the method, a long-span cable-stayed bridge was analyzed.

Picoscopy Discoveries of the Binary Atomic Structure

In this article, we present a discovery of the binary atomic structure. Through picoscopy experiments, it was revealed that electronic structure is divided into core and functional structures. Internal chemically neutral electrons form the core of an atom and are spherical in pink, while the outer functional electrons are elongated in green being chemically active. A spherical yellow layer separates these two parts. It significantly simplifies the Schrödinger equation and leads to a solution for all 118 chemical elements. As a result, the Kucherov-Mudryk formula w = n + ¾l was derived. That formula allowed for organizing the periodic table in ascending order of the whole energy where en electron first fills the level with the lowest energy, according to the Minimum Potential Energy general principle of nature.

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes.

A Partitioned Rigid-Element and Interface-Element Method for Rock-Slope-Stability Analysis

The stability analysis of rock slopes has been a prominent topic in the field of rock mechanics, primarily due to the widespread occurrence of discontinuous structural planes in rock masses. Based on this complex characteristic of rock slopes, this paper proposes a novel numerical method, the Partitioned-Rigid-Element and Interface-Element (PRE-IE) method. In the PRE-IE method, the structure is modeled as several rigid bodies and discontinuous structural planes, which are, respectively, divided into partitioned rigid elements and interface elements. Taking the contact force of node pairs and the displacement of the rigid body centroid as mixed variables, according to the principle of minimum potential energy, the governing equations of PRE-IE can be established using the Lagrange multiplier method and then solved using the nonlinear contact iterative method and the incremental method. A classic case study demonstrates that using the failure of all contact node pairs as the criterion for slope failure is appropriate. This criterion is objective and avoids the potential impact of personal bias on safety factor calculations. Two numerical examples of differently shaped slopes are provided to verify the correctness and validity of the PRE-IE method. By comparing the safety factor calculated using the PRE-IE method with those obtained from other different methods, as well as comparing the computational time, it is shown that the PRE-IE method, in combination with the SRM, can accurately and efficiently analyze the stability problems of rock slopes.

General boundary conditions implementation for the static analysis of anisotropic doubly-curved shells resting on a Winkler foundation

In the present work an Equivalent Single Layer (ESL) formulation is proposed for the static analysis of doubly-curved anisotropic structures of arbitrary geometry and variable stiffness resting on a Winkler elastic foundation. In-plane and out-of-plane general distributions of linear elastic springs are provided for the implementation of general external constraints along the edges of the structure. The structure is geometrically described accounting for the principal curvatures of the shell object of analysis. A generalized set of blending functions based on Non-Uniform Rational Basis Spline (NURBS) curves is adopted so that arbitrary shaped structures can be modelled with the same approach. The fundamental governing equations are obtained in terms of displacement field unknowns, which has been effectively described accounting for a unified formulation based on the minimum potential energy principle. General anisotropic lamination schemes are considered, setting a general orientation of each lamina, as well as all possible material symmetries. The numerical implementation is performed by means of the Generalized Differential Quadrature (GDQ) method, thus allowing a strong formulation of the structural problem. A series of validation examples is performed on shells with zero, single and double curvatures in which the static structural response provided with the proposed formulation has been compared to that obtained from a refined three-dimensional finite element model, showing a great accordance between these different approaches. The research shows that the employment of higher order theories, together with the GDQ method, allows to obtain very accurate results with a reduced computational cost, compared to finite element simulations.

A parametric study on influence of slenderness ratio on the nonlinear dynamic behaviour of rotating tapered beams

In the present work, the effect of slenderness ratio on the nonlinear vibration attributes of the rotating tapered cantilever beam in the flap-wise direction is studied. Different variations and combinations of tapered beams like single tapered in depth and breadth direction, unequal and equal double tapered beams are considered for this work. The equations of motion are derived using energy method and subsequently nonlinear governing equations are solved using the framework of minimum potential energy with the help of trail functions. Geometric non linearity caused by large amplitude vibration is considered an iterative algorithm is adopted to solve for the nonlinear governing equations. The results obtained are quite accurate and matching with some available results. Furthermore, the effect of nonlinearity on the vibration attributes of the tapered beams with different combinations for different slenderness ratios being presented. The algorithm which is adopted to solve the problem, takes less computational time and relatively easy to formulate.

Effect of graphene reinforcement distribution on energy release rate and vibration of thermally pre/post-buckled delaminated composite plates

The nonlinear thermal stability responses of functionally graded graphene-reinforced composite (FG-GRC) laminated plates with single or multiple through-the-width delaminations, are investigated in the article. The possibility of delamination growth is evaluated using the three-dimensional crack tip element (3D-CTE) method, which determines the energy release rate (ERR) at the delamination edge. Furthermore, the influence of delamination configurations and the types of graphene reinforcement distribution patterns, on the free vibration of FG-GRC delaminated plates in thermally pre/post-buckled regimes is evaluated. The von Karman geometrical nonlinearity is adopted in a solution based on the layerwise third-order shear deformation theory (TSDT). The nonlinear equilibrium equations derived by the minimum total potential energy principle are solved using the Ritz method in conjunction with the Newton–Raphson iterative procedure. A three-dimensional finite element model is also developed using ABAQUS to corroborate the accuracy of the theoretical results. Parametric studies reveal that while the FGX graphene distribution pattern improves the bending stiffness of delaminated composite plates more than FGA, the ERR at the near surface delamination edge in FGX pattern is twice as high as that in FGA. This implies that the possibility of delamination propagation in FGX plates can be higher than FGA. Additionally, while the fundamental frequency of the FGX plate with and without delamination exceeds the frequency of other graphene distribution patterns at the reference temperature, its natural frequency is the lowest among all patterns in the post-buckled regime.

Unified buckling computational framework of hydro-statically-loaded stiffened composite cylindrical shells

In this research, a unified computational framework was developed to analyze the complex multiple buckling modes of stiffened cylindrical shells under hydrostatic pressure, and avoid the complex process of calculating multiple buckling modes separately by traditional methods. The stiffener-shell displacement constraints were analyzed through introducing stress distribution to the shell. The minimum potential energy principle was adopted for the buckling load solution. The framework can predict the overall buckling, tripping, and coupled shell-stiffener buckling simultaneously, and reveal the relationship between buckling modes and structural dimensions. The unified framework is more convenient and saves computational resources compared with the finite element method. Based on this new method, the buckling mode transition characteristics under simply- and fixed-supported boundary conditions were discussed. An energy-based criterion was proposed to evaluate the occurrence condition of each buckling mode. The research provides a reference for the design of submerged composite stiffened cylindrical shells.

Spatial Deformation Calculation and Parameter Analysis of Pile–Anchor Retaining Structure

Scholars often consider the deformation of a foundation pit retaining structure as a significant indicator of its stability. However, the current theoretical prediction formula for pit with pile–anchorretaining structure deformation is not yet perfect. This study utilizes a simplified spatial deformation model of a pile–anchorretaining structure and the principle of minimum potential energy to derive a prediction formula for the retaining structure’s spatial deformation. Afterwards, a numerical simulation model is developed based on actual engineering practices. On-site monitoring data is compared with the results of theoretical calculation formulas and numerical simulation models to validate their applicability. The research findings reveal minimal discrepancies between the theoretical calculation results, numerical simulation outcomes, and on-site monitoring data, indicating a high level of accuracy. Those three results follow consistent rules. The horizontal deformation curve of the crown beam exhibits a ‘V’-shaped distribution, and as the distance from the calculation point to the centerline of the foundation pit decreases, the horizontal deformation of the crown beam increases. The horizontal deformation curve of the pile displays a ‘V’-shaped distribution, and the pile’s horizontal deformation increases as the distance to the centerline of the foundation pit decreases. The research findings indicate that increasing the size and material strength of the crown beam and waist beam has only a limited effect on controlling the retaining structure’s deformation. However, by increasing the size and material strength of the pile, the deformation of the retaining structure can be significantly reduced.

Impact effect-based dynamics force prediction model of high-speed dry milling UD-CFRP considering size effect

The impact and size effect are generally neglected in force prediction model of cutting Carbon Fiber Reinforced Polymer (CFRP). Since carbon fibers are frequently cut in and out, the main cutting mechanisms of CFRP are mixed by impact, shear and other mechanisms, which are difficult to be clarified. Thus, we establish an impact effect-based cutting force prediction model of CFRP considering size effect. In the model, cutting regions are effected by chipping, pressing, impacting and bouncing, respectively. The cutting force is calculated based on the representative volume element (RVE) and minimum potential energy principle (MPEP). After chip breakage, the free-damped vibration force prediction model is established. The dynamics force prediction model is proofed with high prediction accuracy. Besides, the influences of cutting parameters on impact, cutting and vibration are analyzed by nonlinear regression analysis. It demonstrates that the impact and size effect are of great significance in revealing the cutting mechanisms of CFRP.

Nonlinear static analysis of bi-directional functionally graded sandwich plates in thermal environments by a higher-order finite element model

This study addresses nonlinear static behaviours of bi-directional functionally graded (2D-FGM) sandwich plates lying on an elastic foundation in thermal environments for the first time. The plates comprise two 2D-FGM face sheets and a homogeneous core layer. The material properties of the face sheets change according to the power law in both the longitudinal and thickness directions. Furthermore, the material properties also possess temperature-dependent characteristics in the thermal environment. For the analysis purpose, a higher-order finite element model (FEM) based on Shi’s plate theory that takes into account the geometrically nonlinear von Kármán without regard to material nonlinearity is established. The minimum potential energy principle is used to establish the weak form of governing equations. The four-node rectangular element with the Lagrange and Hermitian interpolation functions is used to discretize the domain of the plate. The nonlinear equilibrium equations are solved by employing Newton–Raphson iterative procedure. The numerical examples comparing the obtained results with the published results in open literature have confirmed the accuracy and convergence of the proposed model. Finally, a few novel parametric studies are conducted to show the effects of the material properties, geometric parameters, temperature, elastic foundation stiffness, and boundary conditions on the nonlinear static behaviours of the 2D-FGM sandwich plates.

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.