Superposition Principle Research Articles

Thermo-elastic analysis for clamped laminated arches subjected to non-uniform temperature boundary conditions

This paper delves into the thermo-mechanical behavior of clamped composite laminated arches exposed to non-uniform thermal environments. Exact solutions for temperature, displacements, and stresses in laminated arches with arbitrary thickness and number of layers are derived based on the theory of thermoelasticity. Given the complexity of the inhomogeneous temperature conditions at the edges, a specialized temperature function is constructed to accurately satisfy the non-homogeneous thermal boundary conditions. On the basis of Fourier’s law of heat conduction and the principle of superposition, the analytical temperature solution is obtained with the transfer matrix method. Clamped support conditions are addressed by incorporating unit pulse functions and Dirac delta functions into the analysis. The state equation is established with displacements and stresses serving as the state variables. According to the continuity conditions at the interfaces and the mechanical conditions on the surfaces of the laminated arch, the exact solutions for displacements and stresses are uniquely determined. The convergence and comparison studies confirm the efficacy and accuracy of the proposed method. Furthermore, three detailed numerical examples are presented to explore the effects of surface temperature, thickness-to-radius ratios, material properties, and layer numbers on the distributions of temperature, displacements, and stresses within the laminated arches.

Adhesion-induced roof collapse of a rectangular micro-groove under applied pressure

ABSTRACT In soft lithography roof collapse is frequently observed on the stamp surface consisting of rectangular micro-grooves which yields unwanted contact between the sagged surface and the substrate. Deep understanding of the adhesive contact behavior is a key to design of high-performance collapse-resistant stamp. Both theoretical and numerical studies are presented for a single rectangular micro-groove in the middle of the stamp surface under applied pressure. The JKR-type adhesion solution is established by the principle of superposition and equivalent energy release rate, with a series of closed-form expressions derived which are consistent with previous studies. Finite element analysis (FEA) is performed based on virtual crack closure technique (VCCT) to investigate the roof collapse mechanism with interfacial adhesion and applied pressure considered. Comparison of theoretical, numerical, and experimental results demonstrates that both size effect and constitutive nonlinearity of the stamp on the self-collapse contact width are not obvious for shallow grooves but become prominent for deep grooves, so that the obtained analytical solution is limited to shallow grooves due to its assumptions of half-plane and linear elasticity adopted for the stamp. For deep grooves, the present FEA method shows potential to capture more accurate results.

Bedding and bedding surfaces in carbonate and mixed carbonate–siliciclastic successions part 2: processes, identification and implications of diagenetic bedding

Bedding and bedding surfaces in carbonate and mixed siliciclastic–carbonate successions can be diagenetic, not depositional, in origin and require interrogation to determine their true origins. This study reviews the different models and implications associated with diagenetic bedding and diagenetic bedding surfaces in such successions. Weathering, especially where strong lithological and mechanical differences occur, can make distinguishing primary and diagenetic bedding more difficult, and criteria are reviewed. Early, shallow diagenetic processes linked to mineral instability of aragonite, mediated by biochemical processes, are capable of producing bedding and bedding surfaces. Zones of early cementation within sediments can produce discrete beds and surfaces exemplified in the formation of limestone–marl alternations (LMAs). Variations in the degree of early cementation (‘stratified cementation’) in shallow buried argillaceous carbonate sediments affected by later compaction can produce layering, with beds showing little compaction separated by highly compacted, argillaceous fissile interbeds which develop bedding surfaces within those fissile units (‘couplets’). Where such diagenetic limestone beds form intrastratally, as in LMAs, they do not obey the principle of superposition and, by virtue of never having been deposited laterally adjacent to their associated deposits, do not comply with Walther's Law of Facies. Bedding surfaces associated with LMAs only become true surfaces when exhumed to produce some types of firmgrounds and hardgrounds.

Elasticity solution of fixed beams under linear temperature variation: An experimental and numerical study

This article presents the Airy stress function method for predicting the structural response of a fixed beam subjected to a linear temperature distribution, using the superposition principle. In this approach, the fixed-end beam is decomposed into three simply supported beams with unknown reactions and a linear temperature variation. For each loading condition, the suitable Airy’s stress functions were formulated to satisfy the stress equilibrium and strain compatibility equations. The results obtained using this method are subsequently contrasted with those derived from finite element modeling. To validate the analytical and experimental results, two finite element modeling approaches, namely two-dimensional and three-dimensional modeling, are implemented using the ANSYS finite element software. This numerical modeling approach utilizes a sequentially coupled steady-state thermal and static structural analysis. In addition to employing Airy’s stress function method and finite element analysis, experiments were conducted on SS304 rectangular specimens under proper insulation to investigate their thermal bowing response. Samples were tested in a simple thermal bending experimental setup under fixed support conditions, and subjected to conduction-type heating to achieve linear temperature changes along their depth. The analytical method predicts that the beam will not deflect under linear temperature variation in a fixed-beam situation. The numerical analysis results confirm this, showing a minimal deflection, that aligns well with the Airy’s stress function method. However, the deflection measured in the experimental program is significantly larger than the predictions from the analytical method. This method eliminates the complexity involved in applying boundary conditions along with thermal loading on a fixed beam.

A Possible Solution to the Black Hole Information Paradox

The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by developing an understanding of the process by which spontaneous symmetry breaks when a black hole selects one of the many possible ground states and emits radiation as a consequence of it. Here, the particle operator number is the order parameter. This mechanism explains the connection between the density matrix, corresponding to the pure state describing the black hole state, and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover black hole information from the superposition principle, applied to the different possible order parameters (particle number operators).

Study on Improving Recovery of Highly Heterogeneous Reservoirs by Unsteady Water Injection Technology

Unstable water injection can effectively improve the recovery ratio of reservoirs with strong heterogeneity. However, the oil displacement mechanism and the determination method of unstable water injection parameters still need to be clarified, especially for complex fracture reservoirs, which greatly restrict the popularization and development of unstable water injection technology. This paper studies unstable water injection technology in highly heterogeneous reservoirs from the core and reservoir scales, utilizing many displacement experiments and numerical simulations. The differences in oil displacement efficiency, remaining oil distribution, pressure field, and streamlines between continuous water injection and unstable water injection are compared and evaluated. Five flow stages of unstable injection and production are precisely divided, and the microscopic and macroscopic displacement mechanism is clarified. A numerical model of two injection wells and one production is established to determine the best time to implement unstable water injection technology. Based on the principle of pressure superposition, the expression of pressure field distribution between injection and production well in each period of unstable water injection is analytically solved. This formula has provided a new development parameter optimization method aiming at the maximum pressure fluctuation range and optimized the development technology parameters in the water injection process. The results show that precise control injection and production parameters can expand water swept volume, effectively improve the degree of reserve utilization, and improve the recovery of complex reservoirs by 3–7%, which provides a reliable basis for the practical implementation of unstable water injection technology.

Evaluating the impact of rock damage and induced fracture evolution on heat extraction using supercritical carbon dioxide as the working fluid: Semi-analytical model, numerical model, workflow, economic analysis, and field case

Geothermal energy, a clean and renewable source, has garnered significant attention. The excellent physical properties of supercritical carbon dioxide make it an ideal fluid for geothermal development. Fractures act as channels for the efficient seepage and heat transfer of supercritical carbon dioxide. Consequently, the macroscopic fracture damage and evolution induced by the flow of supercritical carbon dioxide impact heat extraction efficiency. Here, pseudo-pressure (multi-stage induced fracture and non-Darcy multi-stage fractured) and temperature well-testing (multi-stage induced fracture thermal and non-Darcy multi-stage fractured temperature) models are developed to monitor the fractures evolution during heat transfer. The finite element method, superposition principle, and Duhamel principle are utilized to establish the proposed models. Numerical models that either consider or disregard rock damage and fracture evolution are developed to simulate and compare the efficiency of heat extraction. The COMSOL Multiphysics 6.1 software is used to solve a heat extraction transient evaluation model. A workflow for utilizing the developed models is proposed, followed by an economic sensitivity analysis. Finally, the models are applied to field cases in the Babbage Oilfield to guide the extraction of geothermal energy. Core displacement experiments are conducted to validate its accuracy, and a differential economic analysis method demonstrates its economic benefits. Results show that the well-testing models invert parameters related to reservoir and fracture evolution. Rock damage and fracture evolution during a heat extraction process are primarily influenced by thermal stress, thermal shock, and pressure-driven effects. As production progresses, fracture permeability and porosity increase, rock elastic modulus decreases, and production temperature drops. Comparing the results with versus without considering rock damage and fracture evolution reveals that their maximum pressure difference is 14% and their maximum temperature difference is 5%. The production pseudo-pressure has the greatest impact on fracture evolution. The injection temperature has the most significant effect on heat extraction efficiency, followed by injection pressure, fracture permeability, and a mass flow rate, with elastic modulus having the least impact. The maximum differential economic benefit for a single horizontal well injection-production system reaches $293,000. Field case studies from the Babbage Oilfield demonstrate the practicality of the developed models and workflow. In summary, the models, workflow, and economic analysis methods proposed in this work provide guidance for engineers in formulating more optimized heat extraction schemes.

Seismic Performance of X-shaped Stud Steel Reinforced Concrete Columns Under Composite Torsion

To investigate the seismic performance of X-shaped steel-reinforced concrete (SSRC) columns subjected to combined torsion, eleven specimens were designed with varying parameters including torsion-to-bending ratio, axial load ratio, steel ratio, longitudinal reinforcement ratio, stirrup reinforcement ratio, and stud spacing. Quasi-static loading tests were conducted to observe the failure process and failure modes. The results indicate that the SSRC column ultimate failure mode is predominantly determined by the stirrup reinforcement ratio, leading to either flexural-torsional failure or torsional failure. The torque-torsion angle hysteresis loops exhibit a pinched, inverted "S" shape, while the moment-displacement hysteresis loops display a more pronounced, spindle-like shape. The axial load ratio and torsion-to-bending ratio exert the most significant influence on the seismic performance of the specimens. As the steel ratio, longitudinal reinforcement ratio, and stirrup reinforcement ratio increase, the ductility, energy dissipation capacity, and other seismic performance indicators of the components improve to varying degrees. Among these parameters, the steel ratio has the most pronounced impact on energy dissipation capacity. When the steel ratio increases from 2.39% to 2.90%, the energy dissipation capacity of the component improves by 36.8%. Reducing the stud spacing appropriately enhances the seismic performance of the component, but excessively sparse or dense stud spacing can have detrimental effects. Based on the experimental results and existing research, a formula for calculating the torsional capacity of X-shaped SSRC columns subjected to combined torsion was developed using the superposition principle. The calculated results align well with the experimental results, with an average error within 5%.

The Hartman-Grobman theorem for mean hyperbolic systems

The Hartman-Grobman theorem for mean hyperbolic systems

PARAMETRIC DESIGN AND ADAPTIVE SIZING OF LATTICE STRUCTURES FOR 3D ADDITIVE MANUFACTURING

The present research is developed into the realm of industrial design engineering and additive manufacturing by introducing a parametric design model and adaptive mechanical analysis for a new lattice structure, with a focus on 3D additive manufacturing of complex parts. Focusing on the land-scape of complex parts additive manufacturing, this research proposes geometric parameterization, mechanical adaptive sizing, and numerical validation of a novel lattice structure to optimize the final printed part volume and mass, as well as its structural rigidity. The topology of the lattice structures exhibited pyramidal geometry. Complete parameterization of the lattice structure ensures that the known geometric parameters adjust to defined restrictions, enabling dynamic adaptability based on its load states and boundary conditions, thereby enhancing its mechanical performance. The core methodology integrates analytical automation with mechanical analysis by employing a model based in two-dimensional beam elements. The dimensioning of the lattice structure is analyzed using rigidity models of its sub-elements, providing an evaluation of its global structural behavior after applying the superposition principle. Numerical validation was performed to validate the proposed analytical model. This step ensures that the analytical model defined for dimensioning the lattice structure adjusts to its real mechanical behavior and allows its validation. The present manuscript aims to advance additive manufacturing methodologies by offering a systematic and adaptive approach to lattice structure design. Parametric and adaptive techniques foster new industrial design engineering methods, enabling the dynamic tailoring of lattice structures to meet their mechanical demands and enhance their overall efficiency and performance. Keywords: Computer-Aided Design, Industrial Design, Innovative Design, Additive Manufacturing, FEM Simulations

Predicting High-Cycle Fatigue Damage in Viscoelastic Bituminous Materials Using the Time–Strain Superposition Principle

Predicting High-Cycle Fatigue Damage in Viscoelastic Bituminous Materials Using the Time–Strain Superposition Principle

AN INVESTIGATION OF THE FLUOROSILICONE RUBBER THERMO-OXIDATION PROCESS AT HIGH TEMPERATURES

Abstract Fluorosilicone (FVMQ) rubber is commonly used in many military aircraft applications such as seals and gaskets due to its exceptional heat stability, low temperature flexibility and resistance to fuels and oil. In this investigation, a peroxide cured and silica filled FVMQ rubber compound was prepared and subsequently submitted to accelerated heat aging for up to 50 weeks at temperatures between 75 to 250°C. Heat aged samples were then tested for hardness, physical property characteristics and crosslink density by solvent swell and Double Quantum – Nuclear Magnetic Resonance (DQ NMR). The Arrhenius methodology was applied to the shifted experimental data assuming the principle of time-temperature superposition. The tensile strength and elongation at break both decrease upon thermal treatment. A small stiffness increase was observed by both the hardness and the tensile stress at 10% elongation test data. The characterization of the crosslink density by solvent swell testing was inconclusive. On the other hand, the DQ NMR testing clearly showed that the crosslink density decreases while the number of chain defects increases. The unaged crosslink distribution is heterogeneous in nature displaying much more heterogeneity than peroxide cured silicone. Non-linear Arrhenius behavior was observed between 75 to 250°C with a mechanism change at 175°C. The FVMQ crosslink distribution becomes more heterogeneous with aging. A significant loss of low molecular weight FVMQ due to depolymerization and backbiting reactions was observed at higher aging temperatures. Reactions with the silica surface also occurred with the creation of Si-O bonds. No direct evidence of thermo-oxidative and oxygenation reactions was observed. Reaction mechanisms have been proposed to explain the degradation of FVMQ due to heat aging.

Analytical Solutions for Thermo-Mechanical Coupling Bending of Cross-Laminated Timber Panels

This study presents analytical solutions grounded in three-dimensional (3D) thermo-elasticity theory to predict the bending behavior of cross-laminated timber (CLT) panels under thermo-mechanical conditions, incorporating the orthotropic and temperature-dependent properties of wood. The model initially utilizes Fourier series expansion based on heat transfer theory to address non-uniform temperature distributions. By restructuring the governing equations into eigenvalue equations, the general solutions for stresses and displacements in the CLT panel are derived, with coefficients determined through the transfer matrix method. A comparative analysis shows that the proposed solution aligns well with finite element results while offering superior computational efficiency. The solution based on the plane section assumption closely matches the proposed solution for thinner panels; however, discrepancies increase as panel thickness rises. Finally, this study explores the thermo-mechanical bending behavior of the CLT panel and proposes a modified superposition principle. The parameter study indicates that the normal stress is mainly affected by modulus and thermal expansion coefficients, while the deflection of the panel is largely dependent on thermal expansion coefficients but less affected by modulus.

Exact Analytical Solution of the Problem of Elastic Bending of a Multilayer Beam with a Normal Trapezoidal Load

An exact analytical solution to the problem of plane transverse bending of a section of a narrow multilayer beam under the action of a normal load on the longitudinal faces, distributed according to the law of the trapezoid, is presented. The solution is constructed using the principle of superposition on the basis of the authors’ general solutions to the problems of bending multilayer consoles under the action of loads at the free end, uniformly and linearly distributed load on longitudinal faces. On its basis, separate interchanges for multilayer beams with different methods of fixing the ends were obtained: hinged, rigid and combined. The obtained relations make it possible to determine the stress-strain state of multilayer beams with an arbitrary number of homogeneous (orthotropic, isotropic) and functional-gradient layers, taking into account transverse shear and compression deformations.

Propagation of nonstationary boundary disturbances in a half-plane filled with a homogeneous isotropic elastic medium

This study presents a method for addressing dynamic issues using an elastic half-plane subjected to different sorts of boundary disturbances. The motion of the half-plane is governed by wave equations that pertain to the scalar and non-zero components of the vector elastic displacement potentials. It is assumed that the starting circumstances are zero. An explicit solution to the problem is obtained by using the integral relation between the components of displacements and stresses of the half-plane boundary. This relation is expressed as a two-dimensional convolution with the influence function resulting from the principle of superposition. The properties of the convolution operation in two variables and the theory of generalized functions are used to derive the solution in integral form. Simultaneously, the acquisition of this solution relies on the technique of decomposing the influence function, whereby it is expressed as the multiplication of two components that meet the predetermined essential criteria. Hence, to get conclusive outcomes, it is important to factorize the impact function that has the given characteristics. The process of obtaining the necessary factorization of the influence function relies on describing its image as a multiplication of individual elements. The first derivation of this function was accomplished by the use of the joint inversion technique of the Fourier-Laplace transform, relying on analytical representations of pictures. Consequently, explicit integral formulae were derived to solve the issue and enable the determination of unknown displacements and stresses at any speed range of motion of the boundary conditions interface point. An example of a particular sort of boundary condition is provided to demonstrate the technique for addressing common situations.

Analysis of numerical models of an integral bridge resting on an elastic half-space

Abstract The paper presents three methods of the numerical modeling of a 60 m long integral bridge structure resting on an elastic half-space. For the analysis, three bridge models were built using Abaqus FEA software. Models A and C represent complex three-dimensional numerical models consisting of the bridge structure and the soil layer beneath it. The soil layer on which the bridge is resting was modeled as a homogeneous, isotropic, continuous, and elastic semi-infinite body elastic half-space. Model B represents a simple three-dimensional numerical model consisting of just the bridge structure. The stiffness of the soil layer beneath the structure in model B was modeled with spring constants derived for shallow footing foundation based on the theory for an elastic half-space. This model represents an engineering approach to the design of an integral bridge. In all models, the bridge deck is monolithically connected with abutment walls and intermediate piers. The bridge is made of cast-in-situ reinforced concrete. All material constants used in the analysis are presented in the table. Self-weight, uniformly distributed load, and thermal longitudinal expansion of the bridge deck were applied to the bridge models. Due to the nonlinear boundary condition used in the supports of the bridge model A, such as contact and friction, the superposition principle cannot be used in the calculations of this model. For this reason, all the loads involved in all bridge models were combined into a single load case and the large displacement formulation was used in the static analysis. The self-weight of the soil layer beneath the structure was omitted in the analysis. The author is focused on the method of modeling an integral bridge structure resting on elastic soil. For the purpose of this paper, only two piers from each model were selected, from which the internal forces and displacements were compared. Based on the analysis, it was concluded that it is possible to design an integral bridge by building its simplified numerical model, once the conditions given in the conclusions are met.

Axial Compression Performance Test and Bearing Capacity Calculation Method of Square Steel Tube–Timber–Concrete Composite L-Shaped Columns

The square steel tube–timber–concrete composite L-shaped columns are lighter in weight due to the inclusion of wood and exhibit superior seismic performance. This combination not only reduces transportation and labor costs but also enhances earthquake resistance. The wood contributes lightness and flexibility, the steel provides strength, and the concrete offers excellent compressive performance, thereby achieving an optimized design for performance. To investigate the axial compression performance of square steel tube–timber–concrete composite L-shaped short columns, axial compression tests were conducted on eight groups of L-shaped columns. The study examined ultimate load, failure modes, load–displacement relationships, initial stiffness, ductility, and bearing capacity improvement factors under different slenderness ratios, steel tube wall thicknesses, and wood content rates. The results show that the mechanical performance of the composite columns is excellent. Local buckling of the steel tube is the primary failure mode, with ‘bulging bands’ forming at the middle and ends. When the wood content reaches 25%, the synergy between the steel tube, concrete, and wood is optimal, significantly enhancing ductility and bearing capacity. The ductility of the specimen increased by 31.1%, and the bearing capacity increased by 4.14%. The bearing capacity increases with the steel tube wall thickness but decreases with increasing slenderness ratio. Additionally, based on the Mander principle and considering the partitioned constraint effects of concrete, a simplified calculation method for the axial compressive bearing capacity was proposed using the superposition principle. This method was validated to match well with the test results and can provide a reference for the design and application of these composite L-shaped columns.

Application of the spectral determination method to unified β-, γ- and X-ray spectra

ABSTRACT So far, we have developed the innovative radioactivity quantification technique of spectral determination method (SDM) and applied it to spectra measured with Ge, NaI detectors and liquid scintillation counter (LSC). In the present study we extended the SDM to apply to a unified spectrum composed of LSC and Ge detector, and the number of nuclides has been increased from 8 or 9 to 40. We selected 40 radionuclides from possible radionuclides included in nuclear debris and radioactive wastes in the environment which were produced by the nuclear accident in Fukushima in 2011. We prepared LSC and Ge standard spectra by direct measurements and simulation calculations utilizing the Geant 4.10.3 Monte Carlo simulation tool kit. The derived LSC and Ge spectra for each nuclide were unified to a single spectrum and the 40 sets of them were completed as a unified database. We studied the determination accuracy of the present analysis by examining a composed spectrum made of 40 radionuclides with equal intensities. The SDM result shows that the relative determination uncertainties of 35 nuclides are below 20%. It is also indicated that by removing 3 interfering nuclides the determination accuracy of the other 37 nuclides could be improved.

Analysis of plate oscillatory motion in a variable air flow for power generation

This paper investigates the translational oscillatory motion of a single-degree-of-freedom thin plate under variable airflow conditions, including wind gusts, harmonic flow, and airflow with random parameters. The proposed airflow device is designed as a swing pendulum, where the plate is connected to a fixed base by two identical cranks, with a power generator attached to the end of one crank axle. The rotary motion of the cranks due to airflow is evaluated using an energy dissipation parameter. The interaction between the airflow and the plate undergoing translational (i.e., non-rotational) motion is studied numerically through computer simulations, applying the principle of superposition. In this approach, the fast chaotic motion of air particles (Brownian motion) is separated from the slower flow motion. The modeling incorporates the concept of pressure (downwind) and suction (upwind) zones for a rigid body immersed in an airflow. The analytical formulas derived from these calculations are then used to analyze the motion of the electromechanical system. System parameters are optimized, using generated power as the evaluation criterion. Numerical results confirm the feasibility and efficiency of the proposed wind energy system under non-stationary airflow conditions. The device is suitable for installation in open fields, on building rooftops, along highways, or in tunnels. It is environmentally friendly and poses no harm to people.

Polarization-Independent Focusing Vortex Beam Generation Based on Ultra-Thin Spiral Diffractive Lens on Fiber End-Facet

An ultra-thin spiral diffractive lens (SDL) was fabricated by using focused ion beam milling on a fiber end-facet coated with a 100 nm thick Au film. Focusing vortex beams (FVBs) were successfully excited by the SDLs due to the coherent superposition of diffracted waves and their azimuth dependence of the phase accumulated from the spiral aperture to the beam axis. The polarization and phase characteristics of the FVBs were experimentally investigated. Results show that the input beams with various polarization states were converted to FVBs, whose polarization states were the same as those of the input beams. Furthermore, the focal length of the SDL and the in-tensity and phase distribution at the focus spot of the FVBs were numerically simulated by the FDTD method in the ultra-wide near-infrared waveband from 1300 nm to 1800 nm. The focal length was tuned from 21.8 μm to 14.7 μm, the intensity profiles exhibited a doughnut-like shape, and the vortex phase was converted throughout the broadband range. The devices are expected to be candidates for widespread applications including optical communications, optical imaging, and optical tweezers.