Principle Of Minimum Energy Research Articles

Thermodynamic Analysis of Wetting Transitions on Micro/Nanopillared Superhydrophobic Surfaces

The low adhesion of water drops on superhydrophobic surfaces is a prerequisite for their widespread potential industrial applications. The wetting transition between different wetting states significantly influences the dynamic behavior of water drops on solid surfaces. Although some theoretical studies have addressed wetting transitions, the underlying mechanisms by which local micro- and nanostructure parameters on superhydrophobic surfaces affect the wetting transition have not been fully elucidated. This study investigates three-dimensional micropillared and micro/nanopillared superhydrophobic surfaces, deriving thermodynamically the equation for the free energy barrier of wetting transition, which is influenced by the overall roughness of the entire superhydrophobic surface and its local micro/nanostructures. Theoretical calculations are performed to investigate the effects of various micro- and nanostructure parameters on the free energy barrier and wetting transition. Based on the principle of energy minimization and the calculated free energy barrier, the possible wetting states on superhydrophobic surfaces are analyzed and compared with experimental results. This study contributes to the theoretical understanding of wetting transitions and may guide the design of superhydrophobic surfaces for diverse applications.

Thermal buckling of composite laminates with elastic boundaries

AbstractThe investigation of thermal buckling in composite laminates holds significant theoretical and practical implications. For the commonly encountered rectangular thin plate structures in engineering, this study aims to explore their buckling characteristics under thermal loads in arbitrary elastic boundary conditions. To achieve this, a method based on the principle of minimum potential energy for calculating the buckling load during elastic instability is presented. Initially, transverse constraint springs and rotational constraint springs are set at the four boundaries of the plate structure model, with the stiffness values of these two types of elastic springs designated to simulate arbitrary elastic boundary conditions. The improved Fourier series is employed to address potential discontinuities in the boundary derivatives of displacement functions that may arise with the classical Fourier series form. Subsequently, the potential energy expression for the rectangular plate system is established. By combining this with the principle of minimum potential energy, a system of linear equations is derived through partial differentiation of the unknown Fourier coefficients. Finally, the critical buckling load and other parameters of the rectangular plate are obtained, with reasonable values for the spring stiffness under different boundary conditions provided. The critical buckling temperatures derived from the proposed method are compared with those obtained via finite element analysis. The results indicate that the buckling loads obtained using this method align closely with those from finite element analysis, affirming the validity and convergence of the research methodology.Highlights This study investigates the thermal buckling of composite laminate plates with elastic boundary conditions. Improved Fourier series techniques are employed to analyze thermal buckling in these laminates. The impact of intermediate stiffness on the thermal buckling response of composite materials is examined.

Analysis and optimization for buckling behavior of functionally graded face layers and porous core sandwich plates resting on pasternak elastic foundation

In this paper, the first-order shear deformation theory (FSDT) is employed to derive analytical solutions for the buckling analysis of functionally graded material—porous—functionally graded material (FGM-porous-FGM) sandwich plate resting on Pasternak elastic foundation. The top and bottom layers of the plate consist of functionally graded materials that vary according to the exponential law along the thickness direction, while the core layer is composed of a porous material. The governing equations are derived by using the principle of minimum total potential energy. Based on the Navier’s solution, the displacements are obtained to satisfy the boundary conditions. The results are then compared with existing published literature showing the accuracy of the proposed solutions. Moreover, parametric studies investigate the effects of material parameters, geometric dimensions, foundation coefficients and face-core-face thickness ratios on the critical buckling load of the rectangular FGM-porous-FGM sandwich plate. In the case of uniaxial loading, the critical bucking load is almost twice for the case of biaxial loading, no matter the value of volume fraction index. For all the cases of face-core-face thickness ratio, the biaxial critical buckling load linearly depends on the porosity coefficient. The porosity coefficient is crucial when and only when the volume of the core is almost eight times bigger than the volume of the face layer. Optimization studies are then presented in order to: (i) maximize the critical buckling load and (ii) optimize the input variables corresponding to a given value of the critical buckling load. The proposed study aims to provide valuable insights into the design and application of FGM-porous-FGM sandwich plates in various engineering fields, contributing to the development of more resilient and efficient structural components.

Impact and analysis of corrosion on elastic stress in a composite disk under parabolic temperature distribution using the Rayleigh-Ritz method with trigonometric Ritz functions

This study conducts an in-depth impact and analysis of corrosion on the elastic stresses within a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is modeled as a thermo-elastic composite material to evaluate its performance under thermal and corrosive conditions. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for both radial and tangential stresses. This method applies the principle of minimum potential energy to approximate displacement fields through Trigonometric Ritz Functions, which are subsequently employed to calculate stress components. The parabolic temperature distribution imposes a non-uniform thermal load across the disk, significantly altering the stress distribution. The study explores how the inherent thermal properties of the composite material interact with temperature variations, resulting in intricate stress patterns. By systematically varying temperature parameters, the analysis uncovers the sensitivity of stress components to thermal gradients. Comparative evaluations are performed for different temperature profiles, identifying critical regions of stress concentration. The findings offer essential insights into the behavior of thermo-elastic composites under non-uniform thermal and corrosive conditions, establishing a robust analytical framework for future research and practical engineering applications. This research emphasizes the necessity of integrating both thermal effects and Trigonometric Ritz Functions in the design and analysis of composite structures exposed to varying temperature loads and corrosion.

Analysis of elastic stresses and thermal creep effect for a composite disk under the parabolic distribution of temperature using the Rayleigh-Ritz method with trigonometric Ritz functions

This research provides a detailed examination of the thermal creep effect on elastic stresses in a composite disk exposed to a parabolic temperature distribution. The disk, reinforced with steel fibers, is treated as a thermo-elastic composite material. The Rayleigh-Ritz method, a widely recognized numerical approach for solving boundary value problems, is utilized to derive analytical solutions for the radial and tangential stresses. This method employs the principle of minimum potential energy to approximate displacement fields using Trigonometric Ritz Functions, which are subsequently applied to calculate the stress components. The parabolic temperature distribution imparts a non-uniform thermal load across the disk, significantly affecting the stress distribution. The study explores how the thermal creep effect, intrinsic to the composite material, interacts with thermal variations, resulting in intricate stress patterns. By adjusting temperature parameters, the analysis demonstrates the sensitivity of stress components to thermal gradients. Comparative assessments are performed for various temperature profiles, identifying critical areas of stress concentration. The findings offer significant insights into the behavior of thermo-elastic composites under non-uniform thermal conditions, providing a robust analytical foundation for future research and engineering applications. This research emphasizes the necessity of considering both thermal creep effects and Trigonometric Ritz Functions in the design and analysis of composite structures subjected to varying temperature loads.

Minimum energy principles in electrostatics

Abstract We employ the principle of minimum energy of the electrostatic field to derive Laplace’s equation for electric potential in charge-free space. We also apply the principle of minimum electrical potential energy of a system of discrete charges to explain the possibility of the existence of their stable equilibrium configuration on the surface of a conductor.

A hyperelastic constitutive model for soft elastomers considering the entanglement-dependent finite extensibility

In this paper, a novel hyperelastic constitutive model for soft elastomers is developed based on the concept of the tortuous tube. This model incorporates the finite extensibility of the polymer chain, the entanglement contribution to elasticity and the non-affine micro-to-macro scale transition in a unified way. To reflect the entanglement effect and its influence on the deformation of soft elastomers, the tortuous tube concept is introduced. The finite extensibility and conformational statistics of an entangled polymer chain in such a tortuous tube are clarified. By embedding the tortuous tube into the microsphere and employing the principle of minimum averaged free energy, a new non-affine scale transition rule is proposed to establish the relationship between the local deformation of a polymer chain at the microscopic scale and the overall deformation at the macroscopic scale. Based on the probability density function related to the conformational statistics, the Helmholtz free energy is established and further decoupled into a volumetric part and an isochoric part. The spatial Kirchhoff stress tensor and spatial elasticity tensor are derived from the newly established Helmholtz free energy. The proposed model is further implemented into the finite element program ABAQUS by writing a user-defined material subroutine. The prediction capability of the proposed model is verified by simulating the homogeneous and inhomogeneous deformations of soft elastomers under various loading modes, including uniaxial tension, uniaxial compression, pure shear, equi-biaxial tension, general biaxial tensile loadings, inflation and indentation. Moreover, the influence of entanglement concentration on the stretchability and stiffness of soft elastomers is predicted and discussed using the proposed model.

Modifying the refined zigzag theory to incorporate functional gradation into the bending analysis of laminated beams

Extensive research has been conducted in the field of composite materials, particularly in laminated composites. However, laminated composites often face challenges such as stress concentration at interfaces due to the sharp differences in properties between layers. This study proposes an approach to mitigate stress concentrations in laminated composites using functionally graded materials (FGM). FGM is achieved by gradually varying properties across the thickness of each beam layer, employing the power law in conjunction with the rule of mixtures. The modeling is based on the refined zigzag theory (RZT), with an additional introduction of the sublayers to capture the functional gradient. The analysis involves deriving the zigzag function for FGM, which is referred to as modified RZT. Subsequently, the kinematic model is applied based on the principle of minimum total energy to derive the Euler equation and its associated boundary conditions. For analytical resolution, the Navier procedure is employed. The results obtained for displacement and tension fields are compared with other formulations from the literature, demonstrating alignment and validation of the proposed method.

Theoretical Analysis of Self-Shrinkage Spheroidization of Irregular Degradable Polymer Powder under Thermodynamic Nonequilibrium State

Laser three-dimensional (3D) printing offers significant advantages in integrating the shape and function of regenerative tissues through biomimetic manufacturing. However, its effectiveness is limited by the lack of specialized biopolymer powders—while solvent methods that use residual solvents produce powders with poor biocompatibility, mechanical methods result in irregularly shaped crystals. In this study, a biopolymer powder spheroidization and shaping technology, which utilizes the evolution of irregular powders into spheres with minimal surface free energy in the molten state, is proposed based on the thermodynamic principle of minimum energy. Initially, the motion trajectory and temperature field of the poly(L-lactic acid) (PLLA) powder during spheroidization were quantitatively assessed and optimized using Stokes’ law and Fourier's principle. Subsequently, the cohesive forces and aggregation kinetics of the polymer chains were calculated using molecular dynamics. Finally, based on these calculations, a phase-field model was constructed to simulate the evolution of the spheroidization rate and deduce the optimal parameters for the process. This precise approach enhances PLLA spheroidization control for laser 3D printing, improves part densification and surface quality, and offers a clean and efficient path for preparing high-quality PLLA spheroidized powder for laser 3D printing.

Dynamic Passivation of Perovskite Films via Gradual Additive Release for Enhanced Solar Cell Efficiency.

Modifying perovskites with functional additives has proven effective in refining the crystallization process and passivating the defects of perovskite films, thereby ensuring high photovoltaic efficiencies. However, conventional methods that involve pre-mixing additives into the precursor solution often face challenges due to discrepancies in the spatial distribution of slow-diffused additives relative to dynamically formed defect sites, resulting in limited passivation effectiveness. To address this issue, this study innovatively proposes a dynamic passivation strategy that utilizes a pre-passivator to gradually release active additives during the thermal crystallization process of perovskite films. By leveraging the principle of energy minimization, these timely-released additives can interact precisely and selectively with the high-energy defect sites generated during crystallization, thus facilitating efficient additive utilization and in situ real-time defect passivation. Through analysis of crystallization kinetics and carrier dynamic, it is demonstrated that this dynamic passivation approach significantly improves film quality and prolongs carrier lifetime, outperforming traditional pre-mixing tactics. Consequently, the final perovskite solar cell achieves an impressive solar conversion efficiency of 25.33%, along with exceptional stability. This work provides strong support of tailored additive strategies aimed at further enhancing the efficiency of perovskite solar cells and their subsequent commercial applications.

Mechanical adjustment and prediction of metal-composite reconfigurable tubes

FML (Fiber metal laminate) is widely used in aerospace as an advanced composite material. Metal hybrid bistable composites are one type of FML structure. The hybrid bistable composite is not only deformable but also conductive. In this paper, based on a bistable metamaterial tube, it is proposed to control its shape through metal-composite layups. A theoretical prediction model with a metal slip effect is developed. The energy equation of the theoretical model was solved using the principle of minimum potential energy. The curvature variation rules of two configurations of composite tube with different metal layups and different initial curvatures are discussed. Moreover, the finite element model of the metal hybrid composite is established. Finally, the accuracy of the theoretical and finite element models was verified by experiments. The proposed metal slip model is accurate than the classical model. The effect of metal on the bistable tube was determined. The configuration of the bistable tube is controlled by layups without adding any weight. This plays an important role in deformable metamaterials and multi-functional morphing structure applications.

Snap-through mechanism of a thin beam confined in a curved constraint

In this work, a novel snap-through mechanism of a thin beam confined in a curved constraint and driven by local loading curvature is investigated. The movable boundaries of the buckled thin beam enable it to output snap-through rotation at a lower energy input than the double-clamped beam structure. A theory is proposed to reveal the snap-through mechanism of the proposed structure based on the principle of minimum potential energy and saddle-node bifurcation, which uncovers the influences of loading positions, length ratio and constraint radius on the critical loading. Both theoretical and experimental results show that the large loading position and small constraint radius correspond to a large critical loading, while the length ratio hardly affects the critical loading. In addition, an experimental device is designed to output linear displacement based on the proposed snap-through mechanism. Due to lower energy input and snap-through response characteristics, the proposed bistable mechanism exhibits great prospects in energy harvesters, actuators, motors, pumps and robots.

Intraoperative interaction modeling between surgical instruments and soft tissues in neurosurgery based on energy functions

A physical model of soft tissue that provides realistic and real-time haptic and visual feedback is crucial for neurosurgical procedures. This paper investigates the interaction between surgical instruments and soft brain tissue, proposing a soft tissue deformation simulation method based on the principle of energy minimization and constrained energy function. The model includes a permanent deformation energy function induced by friction and a volume preservation energy function to more accurately depict tissue response during procedures such as resection of convex meningiomas and evacuation of intracerebral hematomas. Experimental results show that the proposed method meets the requirements of neurosurgical simulation.

Design and photothermal coupling analysis of Kresling origami-based intelligent dynamic shading system

This study investigates the design and mechanical analysis of Kresling origami structures for reconfigurable intelligent dynamic shading system aimed at enhancing energy efficiency and thermal management. A mechanical model was developed using the principle of minimum potential energy, followed by 4D printing of specimens tested under compression, showing strong alignment with theoretical predictions. The research highlights the system's intelligent ventilation capabilities, incorporating adjustable fan blade units into the Kresling structure. Shape Memory Polymer (SMP) enables intelligent folding, while Carbon Fiber Reinforced Polymer (CFRP) ensures structural stability. The photothermal coupling analysis reveals how the system autonomously adjusts the shade angle in response to environmental changes, improving indoor illumination and thermal comfort. This intelligent shading system outperforms conventional permanent solutions, reducing energy consumption and enhancing user comfort, ultimately providing innovative insights for future energy-saving technologies in buildings.

Minimum energy combined and separated bounds on elastic constants of transversely-isotropic composites

The considered linearly-elastic transversely-isotropic composite (TIC) is composed of n isotropic, or more generally, transversely-isotropic components sharing the materials’ common symmetry axis with that of the macroscopic material. Using the basic minimum energy and complementary energy principles with certain free-parameter-dependent mixed-longitudinal-transverse-mode strain and stress trial fields, various combination bounds involving some sets of the macroscopic (effective) mixed-mode elastic constants of the composite, which are inter-connected via the constitutive relations, have been established. Choosing the appropriate parameter values of/or optimizing over the free parameters in those inequalities, the separated bounds on the major effective mixed-transverse-longitudinal-mode elastic constants, including the transverse bulk modulus Keff, the longitudinal Young modulus Eeff, and the longitudinal Poisson’s ratio νeff, are derived, beside the classical arithmetic and harmonic average bounds on the pure-mode ones — the transverse shear (μeff) and longitudinal shear (μ̄eff) moduli. The separated bounds on 4 remaining effective mixed-mode elastic constants are also obtained. The illustrative numerical comparisons of the bounds, in the two component case, with those for the special subclass of unidirectional transversely-isotropic composites (UTIC), having the unidirectional cylindrical boundaries between the component materials parallel to their symmetry axis, and the exact coated-cylinder assemblage and laminate models are presented. The extreme models cover substantial parts between the bounds for TIC; however the laminate models lie outside the bounds for the subclass UTIC.

Static and Transient Response Analysis of Arbitrary Laminated Composite and Sandwich Shells by the FSDT Meshless Method

This paper, for the first time, presents a novel meshless method based on the first-order shear deformation theory (FSDT) and moving-least squares (MLS) approximation to carry out static and transient response analysis on arbitrary laminated and sandwich shell structures. The novelty of the method lies in the implementation of MLS in the curvilinear shell formulation, and the derivation of meshless governing equations on the static and transient response of arbitrary laminated and sandwich shells according to the principle of minimum potential energy and Hamilton’s principle, respectively. The concept of a Convected coordinate system is adopted to deal with arbitrary curvilinear surfaces. Both the position and displacement vectors of shells are approximated by MLS, which is conceptually the same procedure as that in the isoparametric finite element method (FEM). The numerical integration of the stiffness matrices is conducted by the simple Gaussian integral in the Convected coordinate system. Because the moving-least squares (MLS) approximation does not satisfy the Kronecker delta condition, the full transformation method is used to modify the meshless governing equations. Numerical examples are calculated to investigate the static and transient response analysis of laminated and sandwich structures with different geometrical shell shapes, including square plates, spherical shells, doubly-curved shells, and cylindrical shells. The numerical tests show that the proposed method is reliable, and robust and produces accurate results compared to the analytical and numerical solutions taken from the previous literature.

A Variational Approach to Analyze the Settlement of Existing Tunnels Caused by Ground Surcharge

This paper presents a variational approach to assess the settlement of the operational shield tunnels resulting from surface loading. The vertical additional force on the tunnel, induced by the surcharge, was computed using the Boussinesq solution. The structural behavior of the tunnel was modeled using the Timoshenko beam theory, which accounts for both bending and shear deformation mechanisms. Furthermore, the two-parameter Pasternak foundation model, which accounts for the continuity of foundation deformation, was used to model the interaction between the tunnel and the surrounding ground. A finite Fourier series was employed to approximate the vertical displacement and cross-sectional rotation angle of the tunnel. By conducting work and energy analyses, the energy balance equations for the tunnel and the soil were obtained. The governing equations were then formulated according to the minimum potential energy principle. The displacement and cross-sectional rotation angle of the tunnel were then expressed through the variational method. The accuracy of the proposed method was validated by comparison with in situ measurement data, confirming its effectiveness in predicting tunnel responses under a ground surcharge. Finally, a parametric study was conducted to evaluate the impact of various parameters on the settlement of the shield tunnel.

Study on the circumferential tensile behavior of SiCf/SiC composite cladding tubes across a broad temperature range: High temperature interface enhancement effect from a cross-scale perspective

In nuclear reactors, Silicon carbide fiber reinforced silicon carbide matrix (SiCf/SiC CMC) cladding tubes are susceptible to circumferential damage due to internal gas pressure expansion. However, due to its complex spatial fiber winding structure, investigating circumferential tensile failure under extreme temperatures is challenging. Therefore, using cross-scale methods and experiments from 20 °C to 1100 °C, this study examined circumferential damage at macro, micro, and nanoscale levels. Specifically, as the temperature increases, the material still maintains excellent structural stability; at 1100 °C, the critical damage load decreases by 72.5 % and the critical displacement increases by 197.1 %.The " interface enhancement effect" between the fibers and matrix results in a relatively smooth fracture morphology. At the macroscopic level, morphology evolution reflects the transition from brittle to pseudo-plastic behavior. Additionally, based on the principle of minimum potential energy and the theory of semi-geodesics, the complex macroscopic structure and microscopic Representative Volume Element (RVE) model was reconstructed. The findings show the numerical model accurately represents the circumferential damage of SiCf/SiC CMC under extreme temperatures. Simultaneously, at the molecular level, the interfacial strength at high temperature is 7.5 % higher than that at ordinary temperature, resulting in a distinct adhesive interaction between matrix and fibers. This study opens up new avenues for the fundamental theoretical research of such ceramic matrix materials. interface enhancement effect.

Ground movement prediction for twin tunnels with minimum total potential energy principle considering volumetric change of soil

In this paper, a semi-analytical method is developed to solve ground movement due to twin tunnel construction addressing the limitation of zero-volume change in energy method. A novel deformation mechanism, capable of considering the volume change of soil, is developed. Validation of the proposed method is conducted through numerical simulations and field monitoring data. Numerical results indicate the method’s efficacy in accurately describing ground settlement attributed to twin tunneling. Moreover, the proposed method shows improved agreement with the numerical simulation as depth decreases and the prediction performance of the proposed method excels particularly in twin tunnel excavation within clay compared to sand. Furthermore, the method demonstrates superior prediction capabilities at the ground surface compared to the subsurface. Notably, the maximum settlement tends to occur adjacent to the first tunnel. However, it is important to note that increasing the clearance between the twin tunnels diminishes the prediction accuracy of the proposed method.

Three-dimensional buckling analysis of stiffened plates with complex geometries using energy element method

A novel numerical method, energy element method (EEM), is proposed for the three-dimensional (3D) buckling analysis of stiffened plates with complex geometries. The problem is formulated in a cuboidal domain, and any complex geometric stiffened plate is modeled by assigning cutouts within the cuboidal domain. The stiffened plate is considered as an energy body and is discretized using Gauss points with variable stiffness properties to simulate its energy distribution. Incorporating the extended interval integration, Gauss quadrature, variable stiffness properties, and Chebyshev polynomials, the strain energy of stiffened plates with complex geometries can be numerically simulated by putting the stiffness and thickness of Gauss points in the cutouts to zero in the cuboidal domain. Using the principle of minimum potential energy and Ritz solution procedure, the deformation and buckling behaviors of stiffened plates with complex geometries can be captured. As a result of the new formulations in EEM, new standard energy functionals and solving procedures have been developed. In addition, Gauss points are generated within the energy elements accounting for the geometric boundaries of the stiffened plate, which are characterized by level set functions. EEM is employed to investigate complex-shaped stiffened plates with straight or curvilinear stiffeners, and the results are compared to those obtained using FEM or mesh-free method. The precision, generalization, and stability of EEM are demonstrated.