Principle Of Minimum Energy Research Articles

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.

ANALYSIS OF NONLINEAR RIGIDITY CHARACTERISTICS OF AIR BLOWER COMPRESSOR ELASTIC SUPPORTS

Vibrations of rotor systems are largely determined by elastic characteristics of supports. In the general case, the dependence of displacements on force for such supports is nonlinear. This applies to bearing supports of various types. In addition to bearings, elastic elements are also used in supports of rotor systems. They are designed to change the overall stiffness of the supports. The paper analyzes the radial stiffness of flexible ring dampers used in rotor supports. For this, two main approaches are proposed. The first is a conventional simulation of this problem of contact mechanics using the finite element method. The second is an analytical method that can be used as an alternative to expensive numerical calculations. This method is based on the principle of minimum additional energy. A special closed-form variational formulation is developed using the Euler-Bernoulli beam approximation for an elastic ring and a simplified model of normal contact on the ring flanges. It was shown that the surface tolerances of parts have a significant effect on the radial response of a flexible ring, which can become nonlinear. Tight fit of the ring on both sides makes it much stiffer, and non-tight fit leads to free movement of the rotor and much weaker damping of its movement. Both methods gave results that are consistent for the considered cases. By varying their design parameters, it is possible to adjust the rotor systems from critical modes of operation. Keywords: rotor system, elastic support, rigidity, finite element analysis, stress-strain state, contact interaction, principle of minimum additional energy

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.

Bistable behaviour of deployable composite boom with central flat region

This paper studies a new bistable deployable composite boom (Bi-DCB) with central flat region, and it can realize bistable function by storing and releasing strain energy, which has a good application prospect in engineering field. The bistable behaviour of the Bi-DCB with central flat region was investigated through analytical, experimental and numerical methods. Based on the minimum energy principle and three failure criteria, an analytical model for predicting the bistable behaviour of the Bi-DCB with central flat region was developed, including the strain energy, geometric configuration, bistable criterion and stress level. Using the vacuum bag method, a specimen was prepared and the bistable experiment was conducted. In addition, a Finite Element Model (FEM) was presented to model the bistable deformation process of the Bi-DCB with central flat region. Analytical results agreed well with experimental and numerical results. At last, the influence of geometric parameters on the bistable behaviour of the Bi-DCB with central flat region was further investigated with the aid of the analytical model.

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.

Test and Analysis of High-Permeability Material's Microstructure in Magnetic Shielding Device.

The magnetic shielding device is used to provide an extreme weak magnetic field, which plays a key role in variety of fields. Since the high-permeability material constituting the magnetic shielding device determines the magnetic shielding performance, it is important to evaluate the property of the high-permeability material. In this paper, the relationship between the microstructure and the magnetic properties of the high-permeability material is analyzed using minimum free energy principle based on magnetic domain theory, and the test method of the material's microstructure including the material composition, the texture and the grain structure to reflect the magnetic properties is put forward. The test result shows that the grain structure is closely related to the initial permeability and the coercivity, which is highly consistent with the theory. As a result, it provides a more efficient way to evaluate the property of the high-permeability material. The test method proposed in the paper has important significance in the high efficiency sampling inspection of the high-permeability material.

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.

Ferroelectric domain switching pathways—From grain boundary to grain body

Grain boundaries (GBs) are one of the main factors influencing the polar domain evolution of polycrystalline ferroelectrics. However, domain switching from GBs to grains remains an unsolved aspect. Previous microscopic GB assumptions hinder such theoretical investigations, assuming that the structure and properties of GB are independent of the misorientation of adjacent grains. This work investigates the competition between the energy densities and domain-switching pathways based on the formation mechanism of the GB model. It is found that the domain-switching pathways in polycrystalline ferroelectrics follow three rules: (1) domain switching occurs near low-energy-density GBs; (2) the development of domain-switching pathway originates near the low-energy-density GBs. This pathway ultimately influences the overall domain-switching process, which follows the energy minimization principle; and (3) the domain-switching trend expands to both sides of the pathways after complete formation. The domain evolution rules for polycrystalline ferroelectric materials proposed in this work are conducive to improving the performance of ferroelectric ceramics via GB engineering.

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.

Size-dependent thermal bending of bilayer microbeam based on modified couple stress theory and Timoshenko beam theory

The bilayer microbeam can be assigned with two different thermal expansion coefficients, so that the microbeam can be used as a thermal actuator, which can provide bending with thermal loading. As a microdevice, the size effect plays an important role. In addition, the length height ratio L/h of the microbeam has to be smaller than 20, to provide sufficient support. With this ratio, the shear effect of the beam can not be ignored. In this work, considering both the size and shear effects, we modified the couple stress and Timoshenko beam theories to study the thermal bending of bilayer microbeams. By using the principle of minimum potential energy, we derived the higher-order governing equations under thermal load. Then with specified boundary conditions, we adopted the differential quadrature method to solve the governing equations. Finally, using a bilayer microbeam made of aluminum and polysilicon as an example, we verified effects of transverse shear and beam size. Results show that the size effect on beam stiffness is significant when the beam height is on the order of equivalent length scale (leq). Moreover, considering the transverse shear effect indicates that the lateral deflection of the Timoshenko beam depends on the ratio L/h: as L/h increases, the tip deflection increases and converges to the classical solution. Specifically, for a Timoshenko beam with h/leq = 15, the change in deflection can reach 44.6% when L/h is increased from 5 to 25.

A unified variational framework of no-tension and no-compression solids and its application to finite element analysis

No-tension and no-compression constitutive models have important applications in solid mechanics, such as modelling of masonry, wrinkled membrane, unilateral contact interface, etc. Although lots of studies on no-tension and no-compression solids have been found, the variational principle constructing the cornerstone of elasticity is not studied thoroughly. The paper presents two concise variational formulations, a principle of minimum potential energy and a principle of minimum complementary energy, which are available both for no-tension and no-compression solids. Linearization of the conic yield surfaces leads to a series of linear complementary constitutive equations that are embedded into the proposed variational framework. Differing from other variational formulations, an approximate total solution rather than the Newton iteration is achieved in finite element analysis. It makes the algorithm stable. The applications include a no-tension panel benchmark test, two masonry structures and a wrinkled membrane. Compared with our previous study on bi-modulus materials, the newly developed variational formulation is capable of capturing the evolution of wrinkles in membranes, and can be used for the analysis and design of wrinkle-free structures.

饲草收获机动力特性分割优化控制算法研究

In order to improve the level of forage harvester automation and reduce damage, blockage and efficiency, based on the principle of minimum energy, fuzzy prediction theory and external characteristics of power, the mathematical model of the whole machine and each operating unit is established, and a set of forage harvester operating load adaptive feedback control system is designed; in order to make the power more scientifically and effectively distributed in real-time, the system adopts the simplified algorithm of operating unit efficacy threshold load splitting optimization control, with constant power and high efficiency. In order to make the power distribution more scientific and effective in real-time, the system adopts the simplified algorithm of operating unit efficacy threshold load splitting control to increase the load threshold of cutting and other operating units under constant power conditions, so that the operating efficiency of the whole machine can be improved. In the simulation test, the efficacy chopping load threshold ratio is about 1.08:1.01:1 for the three operation control methods of optimized control, fuzzy predictive control and PID control of the forage harvester, with 40% of the original feeding amount perturbation applied respectively. production efficiency was significantly improved.

On simplified deformation gradient theory of modified gradient elastic Kirchhoff–Love plate

A concise modified gradient elastic Kirchhoff–Love plate model with two length-scale parameters is proposed based on simplified deformation gradient theory. A sixth-order basic differential equation and boundary conditions applicable to arbitrary shapes are obtained by applying the principle of minimum potential energy and combining with the generalized strain energy related to classical strain, strain gradient and rotation gradient. By introducing couple stress, the classical bending stiffness corresponding to the fourth-order terms and force-related boundary conditions in the typical gradient elastic Kirchhoff–Love plate model are modified, and the bending deformation of thin plates can be described more flexibly. Under certain conditions, the modified gradient elastic Kirchhoff–Love plate model can be reduced to typical gradient elastic thin plate model, couple stress thin plate model and classical Kirchhoff–Love plate model. The bending boundary value problems of gradient elastic thin plates are further studied, and the specific modified classical boundary conditions and non-classical higher-order boundary condition acceptable to the sixth-order basic equation in Cartesian coordinates are derived. The analytical and numerical bending solutions to gradient Navier-type and Levy-type thin plates with various boundary conditions, including simply supported, clamped and free boundaries are presented, and the size-dependent bending stiffness that is jointly determined by geometric dimensions and length-scale parameters is defined to describe the size effect of thin plates comprehensively.

Superhydrophobicity and compressive stability of Salvinia surface: Mechanical analysis and structural design

The surface of Salvinia had superhydrophobicity and kept good compressive stability, which was mainly attributed to the dense microscopic eggbeater structure villi on the surface. By means of force equilibrium, a theoretical model was established to analyze the interface mechanical behaviors when a droplet infiltrates the microstructures. Based on the minimum energy principle, a theoretical model was presented to analyze the process of a droplet spreading on the surface of Salvinia reaching a steady state. Combined with numerical simulations, it was found that the superhydrophobicity and compressive stability of the Salvinia were dependent on the morphological and geometric parameters of the microstructure (edge angle φ, number of branching n, width W and spacing D, etc.). By adjusting these geometrical parameters, the surface of the biomimetic structure can maintain a stable Cassie state at 0.63 kPa pressure, and the apparent contact angle is controllable in the range of 121°−169.8°. The research results provide a theoretical foundation for the structural design of superhydrophobic surfaces with high stability and tunable wettability.

Buckling Analysis of Composite Piezoelectric Cylindrical Shells with Graphene Skin Subjected to the Axial Load

The buckling of new three‐phase composite shells, which include the base material combined with macro fiber composite and reinforced with graphene (MFC‐GP), is investigated in this article. The bifurcation condition of the buckling is obtained by implementing the first‐order shell theory and wave propagation theory in conjunction with the principle of minimum potential energy. The buckling analysis is transformed into a bifurcation problem of equations. Parametric study is conducted to investigate the effects of the GP volume fraction, length, neutral surface radius, and thickness on the critical buckling loads and critical buckling modes. Furthermore, the influences of voltage and temperature change on the critical buckling displacements are explored. Reliable theoretical support for the design and manufacture of the MFC‐GP structures is provided in the results.

Nonlinear analysis of perforated composite plates under compression by experimental, semi-analytical and numerical methods

The purpose of this paper is to investigate the effects of different cutout shapes on the nonlinear behavior of perforated composite plates using experimental, numerical and semi-analytical methods and to present their capabilities. For analysis, the composite plates are subjected to a compressive load and different out-of-plane boundary conditions are applied to the lateral edges. Investigations are performed by various methods such as experimental tests, finite element method and a semi-analytical technique. For laboratory tests, a fixture has been designed and built that can create different boundary conditions on the lateral edges of perforated plates and can also test laminates up to 6 mm thick. On laminates, three types of openings are created in square, rectangular and elliptical shapes and the perforated laminates are tested with two types of boundary conditions, including clamped on all four edges (CCCC) and simply on two lateral edges and clamped on two ends (SSCC). These experiments are also simulated in the Abaqus finite element package, taking into account the considerations raised and with the nonlinear Riks method. Also, with similar assumptions in experimental and numerical methods, a semi-analytical method has been developed to compare the results and capabilities of different methods in nonlinear analysis of perforated laminates with different boundary conditions. In the last method, the displacement fields are approximated using Legendre functions and assuming the first-order shear deformation theory. Then, the nonlinear system of equilibrium equations governing the perforated plates is obtained through the principle of minimum total potential energy and is solved by the common method of quadratic extrapolation technique. Finally, the capabilities, advantages and disadvantages of each method, especially the fixtures made for this research, are discussed.

Computational Protocol for the Identification of Candidates for Radioastronomical Detection and Its Application to the C3H3NO Family of Isomers

The C3H3NO family of isomers is relevant in astrochemistry, even though its members are still elusive in the interstellar medium. To identify the best candidate for astronomical detection within this family, we developed a new computational protocol based on the minimum-energy principle. This approach aims to identify the most stable isomer of the family and consists of three steps. The first step is an extensive investigation that characterizes the vast number of compounds having the C3H3NO chemical formula, employing density functional theory for this purpose. The second step is an energy refinement, which is used to select isomers and relies on coupled cluster theory. The last step is a structural improvement with a final energy refinement that provides improved energies and a large set of accurate spectroscopic parameters for all isomers lying within 30 kJ mol-1 above the most stable one. According to this protocol, vinylisocyanate is the most stable isomer, followed by oxazole, which is about 5 kJ mol-1 higher in energy. The other stable species are pyruvonitrile, cyanoacetaldehyde, and cyanovinylalcohol. For all of these species, new computed rotational and vibrational spectroscopic data are reported, which complement those already available in the literature or fill current gaps.

Interlayer torsional sliding and strain localization in bilayer graphene

Twisted bilayer graphene can demonstrate extraordinary optical and electrical characteristics due to its interlayer interactions. The strong coupling of normal and tangential van der Waals interactions at the interface results in inhomogeneous interlayer deformations and further changes the bilayer graphene’s physical properties. Herein, theoretical and numerical models are established to study the torsional deformation behaviour of twisting a graphene flake over a rigid graphene substrate. It is found that in-plane deformations have significant influences on the interlayer potential energy density of AA stacking, but seldom affect other stacked domains. The deformation process is thus approximated by first twisting the graphene flake rigidly, and then relaxing the rigid constraints. The bilayer graphene system minimizes its energy by reducing (enlarging) the size of high-energy (low-energy) domains through additional rotations. The additional angles of the graphene flake are derived analytically based on a mechanical model following the principle of minimum potential energy. Results show that the influences of graphene film deformations get significant at small-twist-angles (typically less than 2 ∘ ). This work reveals the torsional deformation evolution mechanism of bilayer graphene and provides beneficial guidance on achieving intriguing physical properties.

Statics and Dynamics of Continuum Robots Based on Cosserat Rods and Optimal Control Theories

This article explores the relationship between optimal control and Cosserat beam theory from the perspective of solving the forward and inverse dynamics (and statics as a subcase) of continuous manipulators and snake-like bioinspired locomotors. By invoking the principle of minimum potential energy and the Gauss principle of least constraint, it is shown that the quasi-static and dynamic evolutions of these robots are the solutions of optimal control problems in the space variable, which can be solved at each step (of loading or time) of a simulation with the shooting method. In addition to offering an alternative viewpoint on several simulation approaches proposed in the recent past, the optimal control viewpoint allows us to improve some of them while providing a better understanding of their numerical properties. The approach and its properties are illustrated through a set of numerical examples validated against a reference simulator.