Complicated deformation simulating on temperature-driven 4D printed bilayer structures based on reduced bilayer plate model

The four-dimensional(4D) printing technology, as a combination of additive manufacturing and smart materials, has attracted increasing research interest in recent years. The bilayer structures printed with smart materials using this technology can realize complicated deformation under some special stimuli due to the material properties.The deformation prediction of bilayer structures can make the design process more rapid and thus is of great importance. However, the previous works on deformation prediction of bilayer structures rarely study the complicated deformations or the influence of the printing process on deformation. Thus, this paper proposes a new method to predict the complicated deformations of temperature-sensitive 4D printed bilayer structures,in particular to the bilayer structures based on temperature-driven shape-memory polymers(SMPs) and fabricated using the fused deposition modeling(FDM) technology. The programming process to the material during printing is revealed and considered in the simulation model. Simulation results are compared with experiments to verify the validity of the method. The advantages of this method are stable convergence and high efficiency,as the three-dimensional(3D) problem is converted to a two-dimensional(2D) problem.The simulation parameters in the model can be further associated with the printing parameters, which shows good application prospect in 4D printed bilayer structure design.

Flutter Analysis of Aircraft Wing Using Equivalent-Plate Models with Orthogonal Polynomials

A method of equivalent simplification,using equivalent-plate models(EPMs),is developed.It is to achieve goals of rapid modeling and effective analysis in structural dynamics and flutter analysis of complex wing structures.It is on the assumption that the wing structures discussed are composed of skin,beams and ribs,and the different plate units(such as skin,beam web,rib web)are not distinguished in modeling,which is to avoid the complex pre-processing and make it more generalized.Taking the effect of transverse shear deformation into consideration,the equivalence is based on the first-order shear deformation theory,and it can import the model files of MSC/NASTRAN and process the information to accomplish the equivalent modeling.The Ritz method is applied with the Legendre polynomials,which is used to define the geometry,structure and displacements of the wing.Particularly,the selection of Legendre polynomials as trial functions brings good accuracy to the modeling and can avoid the ill-conditions.This is in contrast to the EPM method based on the classical plate theory.Through vibration and flutter analysis,the results obtained by using EPM agree well with those obtained by the finite element method,which indicates the accuracy and effectiveness in vibration and flutter analysis of the EPM method.

Flashover Characteristics of Flat Plate Model Under DC Voltage in Wind-sand Condition

The influence of sand dust on discharge of external insulation has caused widespread concern.At present,the research results show wind-sand electricity has a remarkable effect on the discharge characteristics of insulator and has little influence on the discharge characteristics of air gap.The flashover of insulator strings occurs along the insulator surface and air gaps,and the sand dust deposited on the insulator surface may affect the flashover characteristics of insulator strings.This paper studies the flashover characteristics of flat plate model under DC voltage in wind-sand condition.The experimental results show that under positive polarity voltage,the flashover voltage of the flat plate model has a maximum value,while under negative polarity voltage,the flashover voltage of the flat plate model has a minimum value with a certain degree of sand dust deposition.The wind or sand in sand-dust weather has an important effect on the flashover characteristics of the flat plate model.In certain variation range of electric charge,electric charge of sand dust has little effect on the flashover voltage of flat plate model under DC voltage.The deposition of sand has significant influence on the flashover process of flat plate model,which is related to the deposition density and moisture content of sand particle.

Study of Longitudinal Oscillations of a Building on the Basis of Continuum Plate Model

Continuum plate model in the form of a cantilever anisotropic plate developed in the framework of the bimoment theory of plates describing seismic oscillations of buildings is proposed in this paper as a dynamic model of a building. Formulas for the reduced moduli of elasticity, shear and density of the plate model of a building are given. Longitudinal oscillations of a building are studied using the continuum plate and box-like models of the building with Finite Element Model. Numerical results are obtained in the form of graphs, followed by their analysis.

THE PARTIAL PROJECTION METHOD IN THE FINITE ELEMENT DISCRETIZATION OF THE REISSNER-MINDLIN PLATE MODEL

In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.

Modeling of normal faulting in the subducting plates of the Tonga,Japan,Izu-Bonin and Mariana Trenches:implications for near-trench plate weakening

The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.

A rotating elastic plate/block model for Eurasia

On the assumption that a plate is elastically deformable and may rotate as a whole, we found that Eurasian area may be divided into an Eurasian plate and three blocks of the Xiyu, the North China and the Southeast Asia according to tectonic frame of the East and Southeast Asia and the ITRF2008 velocity field in Eurasian area. F tests show that the accuracy of this elastic-plate/block model is significantly higher than the corresponding rigid-plate models; the area covered is notably larger also.

Prediction model of residual stress field in aluminum alloy plate

Residual stress distributions in 7075 aluminum alloy thick plates with different thicknesses and different quenching speeds were measured. A shape function of stress distribution was proposed based on the internal stress distribution characteristics of aluminum alloy. Using nonlinear regression technology,the function between stress value of key points on internal stress curve and surface stress of the plate was obtained. Based on the measured surface stress,stress value of key points and stress distribution shape,the internal stress distribution can be reconstructed. The experiments show that the model is of good engineering practicality.

Thermal modeling and the optimized design of metal plate cooling systems for single concentrator solar cells

A metal plate cooling model for 400~ single concentrator solar cells was established. The effects of the thickness and the radius of the metal plate, and the air environment on the temperature of the solar cells were analyzed in detail. It is shown that the temperature of the solar cells decreased sharply at the beginning, with the increase in the thickness of the metal plate, and then changed more smoothly. When the radius of the metal plate was 4 cm and the thickness increased to 2 mm or thicker, the temperature of the solar cell basically stabilized at about 53℃. Increasing the radius of the metal plate and the convective transfer coefficient made the temperature of the solar cell decrease remarkably. The effects of A1 and Cu as the metal plate material on cooling were analyzed contrastively, and demonstrated the superiority of A1 material for the cooling system. Furthermore, considering cost reduction, space holding and the stress of the system, we optimized the structural design of the metal plate. The simulated results can be referred to the design of the structure for the metal plate. Finally, a method to devise the structure of the metal plate for single concentrator solar cells was given.

A THEORETICAL MODEL OF MAGNETOELASTIC BUCKLING FOR SOFT FERROMAGNETIC THIN PLATES

As an essential model of magnetoelastic interaction between magnetic field and mechanical deformation, the study on magnetoelastic buckling phenomenon of soft ferromagnetic plates in a magnetic environment has been conducted. One of the key steps for the theoretical prediction of the critical magnetic field is how to formulate magnetic force exerted on the magnetized medium. Till today, the theoretical predictions, from theoretical models in publications, of the magnetoelastic buckling of ferromagnetic cantilevered beam-plate in transverse magnetic field are all higher than their experimental data. Sometimes, the discrepancy between them is as high as 100%. In this paper, the macroscope formulation of the magnetic forces is strictly obtained from the microscope Amperion current model. After that, a new theoretical model is established to describe the magnetoelastic buckling phenomenon of ferromagnetic thin plates with geometrically nonlinear deformation in a nonuniform transverse magnetic field. The numerical method for quantitative analysis is employed by combining the finite elemental method for magnetic fields and the finite difference method for deformation of plates. The numerical results obtained from this new theoretical model show that the theoretical predictions of critical values of the buckling magnetic field for the ferromagnetic cantilevered beam-plate are in excellent agreement with their experimental data. By the way, the region of applicability to the Moon-Pao's model, or the couple model, is checked by quantitative results.

Shape model of multi-pass spray deposition plate

Multi- pass spray deposition shows apparent advantages in preparing large scale plates with rapid solidification. Shape model is promoted to obtain excellent shape. Three dimensional mathematical models considering motion of atomization cone and substrate, deposition distance and atomization parameters were used to predict deposited plate’s shape. The results can be used to optimize the process parameters.

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.

Design of scale model of plate-shaped absorber in a wide frequency range

In order to design the scale model in a wide frequency range,a method based on the reflective loss is proposed according to the high-frequency approximation algorithm,and an example of designing the scale model of a plate-shaped absorber is given in this paper.In the example,the frequency of the full-size measurement ranges from 2.0 GHz to 2.4 GHz,the thickness of the full-size absorber is 1 mm and the scale ratio is 1/5.A two-layer scale absorber is obtained by the proposed method.The thickness values of the bottom and top layer are 0.4 mm and 0.5 mm,respectively.Furthermore,the scattering properties of a plate model and an SLICY model are studied by FEKO to verify the effectiveness of the designed scale absorber.Compared with the corresponding values from the theoretical scale model,the average values of the absolute deviations in 10 GHz～12 GHz are 0.53 d Bm^2,0.65 d Bm^2,0.76 d Bm^2 for the plate model and 0.20 d Bm^2,0.95 d Bm^2,0.77 d Bm^2 for the SLICY model while the incident angles are 0°,30°,and 60°,respectively.These deviations fall within the Radar cross section（RCS） measurement tolerance.Thus,the work in this paper has important theoretical and practical significance.

KDD-based rolling schedule model for plate mill

A novel method for generating a rolling schedule is presented, which is fundamentally different from the existing ones. KDD (knowledge discovery in database) techniques are applied for discovering association rules between rolling parameters in a large database of rolling operation, and based on these rules, the schedule for the crucial last six finishing passes is generated. Operational evaluation shows that the schedule generated by the new method outperforms that generated by existing methods. It also shows how in this application the human's domain knowledge is applied to speed up the KDD process and to ensure the validity of the knowledge discovered.

An exact solution for flow past an accelerated horizontal plate in a rotating fluid with the generalized Oldroyd-B model

In this paper, the generalized Oldroyd-B with fractional calculus approach is used. An exact solution in terms of Fox-H function for flow past an accelerated horizontal plate in a rotating fluid is obtained by using discrete Laplace transform method. A comparison among the influence of various parameters in the Oldroyd-B model and the angular velocity of the fluid on the velocity profiles is made through numerical method in graphic form.

OPTIMIZING FORMULATION OF HYBRID MODEL FOR THIN AND MODERATELY THICK PLATES

A 20 - DOF hybrid stress element based upon Mindlin plate theory is developed using the optimization design method for thin and moderately thick plates. Numerical tests consist of the convergency and performance to the plates with arbitrary thickness and shape and of the ultimate thin plate problems.

Modeling the spread of hot-rolled Ni-based alloy plates

The width spread of Ni-based alloy plates in the rolling process is studied. An equation for describing therolling spread of Ni-based alloy plate is proposed based on production data and the Bachtinow equation, which cannot fully account for the compositional variability of Ni-based alloys. To address this, a new coefficient for alloying is added to the equation based on production data. By adding alloying coefficients, it is possible to improve the prediction accuracy for the rolling spread of Ni-based alloy plates and thus better control the width of the rolling spread of different steel grades.