Principle Of Minimum Energy Research Articles

A continuum theory for stripe-shaped magnetic domains in thin films

Starting from a potential-based kinematical description of continuously distributed stripe-shaped domain walls, a mesoscopic potential is derived through an averaging procedure. The resulting mesoscopic theory is formulated in terms of a few fields with physically meaningful microscopic interpretation. Based on a phenomenological closure-domain extension, a constrained energy minimization principle is introduced. A monolithic finite-element based numerical solution algorithm is proposed. Based on a consistent linearization of the numerical algorithm, quadratic convergence is obtained for the nonlinear solution procedure. A first simple examination of the theory is undertaken by simulating a thin film with spatially and temporally non-constant effective anisotropy. The results are found to be consistent with analytical predictions.

Design and modeling of an electro-hydraulic buoyancy adjustment actuator

A lightweight, simple-structured, and fast-response buoyancy adjustment actuator is essential for underwater vehicles. This article presents the design of an electro-hydraulic actuator that can adjust buoyancy by electric stimuli. The buoyancy adjustment approach of the actuator resembles that of the swim bladder, but the electrostatic force, instead of the muscle tension, is applied to expand the volume of the actuator so that the buoyancy changes with the volume when the entire weight of the actuator is fixed. We propose the structural design guidelines and the operating constraints of the actuator by investigating its mechanical model via the minimum energy principle. In the experiment, the actuator shows a maximum 8.58 g buoyancy adjustment ability with a self-weight of 58.6 g. The experimental results also demonstrate that the depth of the actuator in water can be controlled by applying different voltage signals. The electro-hydraulic actuator presents promising potential for future underwater intelligent vehicles in adjusting buoyancy and depth control.

Methodology for determining progressing ultimate states based on the displacement method

Solving of calculation problems for building structures is currently based on the principle of minimum total energy of structures deformation. However, it is not possible to determine the remaining bearing capacity of the structure using this principle. In the study it is proposed to use the criterion of critical levels of deformation energy to solve this problem. As a result, the ultimate state conditions of a design are formulated on the basis of extreme values of generalized parameters of designing over the whole area of their admissible values, including the boundary. The task is solved as a problem of eigenvalues for the stiffness matrix of the system. The extreme values of design parameters that correspond to critical energy levels are found, which are used to find the maximum possible value of the energy of deformation for the considered structure. The residual bearing capacity is calculated by the value of residual potential energy, which, in turn, is equal to the difference between the maximum possible value of the deformation energy of the structure and the work of external forces. A gradual methodology for investigating the progressive ultimate limit state is proposed, which is based on the sequential exclusion of those elements where the onset of the ultimate limit state is expected firstly. An example of the practical use of the proposed methods is given on the example of calculating a simple but visual design - a statically indeterminate truss.

Buckling of constant/variable stiffness curved arbitrary layup composite beams by renewed constitutive relations-based sine finite element with improved in-plane and transverse responses

The elastic stability performance of constant- and variable-stiffness based composite curved beams with general layups is evaluated using an enriched finite element that accounts for three-dimensional structural response features. The variable stiffness is spatially created over the beam by layers with curvilinear fibers. The structural model in the present work is represented by sinusoidal variation based higher-order shear deformable model, augmented with improved in-plane response by zig-zag function and stretching in thickness direction by higher polynomial order. The appropriate constitutive relationships for laminated composite curved beam with arbitrary layup producing stiffness coupling effects are deduced from three-dimensional elasticity relations. The beam governing equations are formed applying the total potential energy minimum principle and the buckling parameters are predicted employing the eigenvalue analysis. The curved laminated beam element efficacy is examined for the known analytical solutions in the literature. Extensive numerical analysis by opting for different structural parameters like curved beam angle, thickness, ply-angle, curvilinear fiber angle variation from center-to-edge, layup, and beam end condition are made to visualize the buckling characteristics of general layup composite curved beams.

Determining folded stable state of bistable deployable composite boom: An improved two-parameter analytical model

The bistable deployable composite boom (Bi-DCB) has garnered considerable interest in the space industry due to its lightweight design, ease of manufacturing, simple structure, and high controllability. In this study, an improved two-parameter analytical model proposed to investigate the folded stable state of the Bi-DCB. The analytical model drew inspiration from the classical Archimedes' helix and utilized the principle of minimum energy to anticipate the folded stable state of the Bi-DCB. Furthermore, two classic failure criteria were utilized to determine the failure indices of six Bi-DCBs in their folded stable state. To verify the accuracy of the improved two-parameter analytical model, a comparison was made between the predicted results and those obtained from both experimental data and two finite element models (FEMs), which demonstrate strong agreement. The results suggest that the Bi-DCB has great potential as a promising alternative for deployable structures, thanks to its superior mechanical properties and ease of deployment.

Design optimization of soft robotic fingers biologically inspired by the fin ray effect with intrinsic force sensing

Soft grippers display adaptability, dexterity, and safety, garnering increased interest in their applications. However, accurately modeling their nonlinear deformation and sensing the grasping force remain challenging. Here, a generalized closed-form kinetostatic model of a biomimetic FRE soft finger is established based on the chained-beam-constraint model. A methodology combining a geometry-based contact constraint technique is presented, utilizing the minimum strain energy principle for sensorless, precise, and rapid estimation of the deformed contours and contact force when the FRE finger grasps an arbitrary object with a continuous surface. Method verification using FEA demonstrates a maximum error of no more than 1.28% and 2.44% for the contour and contact force estimation, respectively. Subsequently, a multiobjective genetic algorithm is used to optimize the FRE finger design for better adaptability and greater grasping force in a special scenario. Finally, the finger's capability to accurately perceive grasping force and deformed contours was demonstrated by four groups of grasping tests using cylinder and cube objects, with maximum average absolute error and relative error of 0.083 N, 9.84%, and 1.335 mm, 10.06%, respectively.

Free-edge effects at circular holes in composite laminates under hygrothermomechanical load

In this paper, the free-edge effects which play an important role in the failure analysis of composite laminates are studied. Pure temperature change and its combination with biaxial tension are investigated for a composite plate with a centric circular hole that is adequately small in comparison to the dimension of the plate. Moreover, the laminate is assumed to be thin, the temperature change of all points of the plate is identical and the biaxial tensile load is applied far from the center of the hole. For this purpose, a semi-analytical method based on a two-dimensional thermoelastic boundary layer theory and a minimum potential energy principle is proposed. It is shown that the present method predicts the interlaminar peeling and shear stresses surrounding the hole with good agreement compared to the results obtained by FEM analysis.

Elasticity and stability of corrugated conical shells with diverse orthotropy

Curved thin-walled structures have attracted significant attention within engineering communities thanks to their remarkable properties, including high load-bearing capacity, tailorable directional stiffness, adaptability, and lightweight characteristics. The geometric intricacies of these structures not only influence their mechanical behavior but also provide a vast design space for exploring new frontiers in structural development. This study investigated a unique form of curved thin-walled structure, namely the corrugated annular conical shell, which exhibits diverse degrees of cylindrical orthotropy across various corrugation patterns. An analytical model was formulated based on the minimum total potential energy principle and first-order shear deformable shell theory to predict the non-monotonous force-deflection relationships and non-uniform stress distributions in corrugated conical shells when axially loaded under compression. Within this novel framework, the local undulation shape, corrugation pitch, and amplitude emerged as influential determinants of the responses of corrugated shells, intrinsically intertwined with the polar and shear orthotropy ratios. The accuracy of our analytical model was verified by comparing its results to those obtained using the finite element method and experimental measurements. A machine learning method was employed to classify the stability behaviors of corrugated annular conical shells and derive comprehensive design maps for the first time. Corrugated annular conical shells hold enticing potential for applications as adaptive spring units or building blocks for more sophisticated architectural metamaterials.

Topology optimization of catalyst bed structure for a solar steam methane reforming reactor aiming at improved conversion efficiency and hydrogen yield

This study optimized the distribution of catalysts porosity for solar steam methane reforming (SMR) reactor using the topology optimization with different objective functions. The optimized structures were similar, wherein dense catalysts were filled in the high-temperature region at the front of the reactor which increased the contact area between reactants and catalysts, and sparse metal foam catalysts were filled at the rear, which was conducive to reducing the flow resistance and facilitating the collection of products. To facilitate the filling in the actual production process, the optimized structure was simplified, and the simplification structure improved the hydrogen production by 6.84%–22.33% and the methane conversion by 6.54%–11.49% under different working conditions compared with the uniform distribution structure. By adjusting the porosity distribution of the catalysts, the temperature field of optimized reactor conformed to the principle of minimum Gibbs free energy (Gmin) and provided guidance for improving the solar SMR reactor performance.

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.

Conformal Theoretical Modeling of Arbitrary Shape Flexible Electronic Sensors Mounted Onto General Curved Surface Substrates

Abstract Stretchable and flexible electronic sensors have been attracted to novel applications due to their conformal integration onto complex curved surfaces, whereas the mounting strains generated by the geometric mismatch of substrate surface and electronic sensors may cause non-conformal contact at the interface, thus would induce non-negligible effects on the performance of sensors. To investigate the influence rules of the shape of electronic sensors and their geometric parameters on conformal contacts, this paper presents a novel conformal model to study the arbitrary shaped films as flexible sensors mounted onto general curved-surface substrates. The energy minimization principle and the integral summation method play vital roles during the modeling, and three types of films with various shapes including rectangular, oval, and hexagonal mounted onto a bicurvature substrate are investigated. The influences of three dimensionless shape parameters of oval and hexagonal film/substrate contacts are analyzed for the dimensionless strain energy of conformal mounting. The strain and critical dimensionless strain energy of three films/bicurvature substrate contacts are calculated and compared under the same conformal area. The results demonstrated that the contour shape of electronic sensor has a considerable effect on conformal mounting and strain. Thus, the developed conformal model would have great significance in guiding the design of flexible electronic devices and sensors when applied to general curved surfaces.

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.

Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates.

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh-Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model's output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.

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.

Optimisation of the operating parameters of a thermal plasma system for the conversion of waste containing polychlorinated biphenyls by thermodynamic modelling

This paper proposes a mathematical modelling approach to determine the thermodynamic equilibrium of chemical systems in order to optimise the operating parameters of the plasma chemical processes in a low-temperature thermal plasma pilot reactor with a direct current electric arc for the treatment of hazardous waste containing polychlorinated biphenyls. The model is primarily based on the principles of mass action and minimum Gibbs free energy. The obtained results can serve as a basis for multi-criteria optimisation based on ecological aspects, reduction of energy consumption and the possibility of using the produced synthetic gas for energy recovery in the process. The analysis carried out clearly showed the advantages of using water vapour as a plasma working medium and the appropriate mixing of the organic waste containing polychlorinated biphenyls with used engine oil for enriched syngas production. The presented analysis determines the optimal reactor temperature for an ecologically efficient treatment and shows possibilities for energy recovery in the process. The proposed model can also be used for other chemical reactors and for the treatment of other chemical substances.

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.

Determination of fracture toughness and yield strength of Inconel 718 by milling operation

This paper presents an analytical scheme to determine the fracture toughness and the yield strength of Inconel 718 by the widely used milling operation. It is noted that there exists material fracture at the tool tip and the removed layer of material undergoes plastic deformation along the primary shear plane. The fracture toughness is considered at the tool tip and the yield strength is applied on the primary shear plane. Subsequently, the modified Williams’ model and the modified Williams-minimization model are both proposed on the basis of the geometries and mechanics in the oblique cutting process. The modelling framework indicates that milling can be developed as an alternative method to determine the fracture toughness and the yield strength from the serrated chip thicknesses combined with the corresponding cutting forces. This is because the experimental method by milling is a convenient scheme as it only requires the cutting forces per unit width of cut with respect to a series of uncut chip thicknesses. In addition, the normal shear angle is predicted by applying the principle of energy minimization. Finally, milling experiments are conducted to validate the two proposed methods. Results show that the two analytical methods return similar values of fracture toughness and yield strength, respectively. Besides, it is noted that high values of yield strength are achieved based on Tresca criterion, which would indicate work hardening in the primary shear zone during the serrated chip formation. The proposed methods exhibit advantages of convenience and generality to derive the fracture toughness and the yield strength, since it is still a challenge for the traditional standard mechanical tests for Inconel 718 due to its toughness and ductility.

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.