Variational principles and governing equations in nano-dielectrics with the flexoelectric effect

The flexoelectric effect is very strong and coupled with large strain gradients for nanoscale dielectrics. At the nanoscale, the electrostatic force cannot be ignored. In this paper, we have established the electric enthalpy variational principle for nanosized dielectrics with the strain gradient and the polarization gradient effect, as well as the effect of the electrostatic force. The complete governing equations, which include the effect of the electrostatic force, are derived from this variational principle, and based on the principle the generalized electrostatic stress is obtained, the generalized electrostatic stress contains the Maxwell stress corresponding to the polarization and strain, and stress related to the polarization gradient and strain gradient. This work provides the basis for the analysis and computations for the electromechanical problems in nanosized dielectric materials.

Study on General Governing Equations of Computational Heat Transfer and Fluid Flow

The governing equations for heat transfer and fluid flow are often formulated in a general formfor the simplification of discretization and programming,which has achieved great success in thermal science and engineering.Based on the analysis of the popular general form of governing equations,we found that energy conservation cannot be guaranteed when specific heat capacity is not constant,which may lead to unreliable results.A new concept of generalized density is put forward,based on which a new general form of governing equations is proposed to guarantee energy conservation.A number of calculation examples have been employed to verify validation and feasibility.

Data-Driven Modeling of Partially Observed Biological Systems

We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.

SOME PROBLEMS IN ELECTROSTRICTIVE AND MAGNETOSTRICTIVE MATERIALS

Some of the previous theories in the electrostrictive and magnetostrictive materials and their differences are discussed in this paper. A variational principle in the general thermodynamic sense is given and the governing equations can be derived from this principle. Illustrational examples are given.

A Singular Perturbation Method for Parametric Investigation on J-lay Installation of Deepwater Pipelines

The maximum bending moment or curvature in the neighborhood of the touch down point （TDP） and the maximum tension at the top are two key parameters to be controlled during deepwater J-lay installation in order to ensure the safety of the pipe-laying operation and the normal operation of the pipelines. In this paper, the non-linear governing differential equation for getting the two parameters during J-lay installation is proposed and solved by use of singular perturbation technique, from which the asymptotic expression of stiffened catenary is obtained and the theoretical expression of its static geometric configuration as well as axial tension and bending moment is derived. Finite element results are applied to verify this method. Parametric investigation is conducted to analyze the influences of the seabed slope, unit weight, flexural stiffness, water depth, and the pipe-laying tower angle on the maximum tension and moment of pipeline by this method, and the results show how to control the installation process by changing individual parameters.

Theory and application of equivalent transformation relationships between plane wave and spherical wave

Based on the governing equations and the equivalent models, we propose an equivalent transformation relationships between a plane wave in a one-dimensional medium and a spherical wave in globular geometry with radially inhomogeneous properties. These equivalent relationships can help us to obtain the analytical solutions of the elastodynamic issues in an inhomogeneous medium. The physical essence of the presented equivalent transformations is the equivalent relationships between the geometry and the material properties. It indicates that the spherical wave problem in globular geometry can be transformed into the plane wave problem in the bar with variable property fields, and its inverse transformation is valid as well. Four different examples of wave motion problems in the inhomogeneous media are solved based on the presented equivalent relationships. We obtain two basic analytical solution forms in Examples I and II, investigate the reflection behavior of inhomogeneous half-space in Example III, and exhibit a special inhomogeneity in Example IV, which can keep the traveling spherical wave in constant amplitude. This study implies that our idea makes solving the associated problem easier.

NONLINEAR BENDING OF SIMPLY SUPPORTED SYMMETRIC LAMINATED CROSS-PLY RECTANGULAR PLATES

Based on the von Karman-type theory of plates, nonlinear bending problems of simply supported symmetric laminated cross-ply rectangular plates under the combined action of pressure and inplane load are investigated in this paper. The solution which satisfies the governing equations and boundary conditions is obtained by using the double Fourier series method.

Study on “J”Type Offshore Pipeline-Laying Method

-Considering both the seabed foundation and wave, an analytic model of 'J' type is proposed for offshore pipeline-laying. The governing differential equation is also obtained for the pipeline on the seabed and for the suspension sections. By utilizing weighted- residual method and dual iteration technique, an approximate solution is obtained, too. In the end, calculation examples are given for analyzing the changeable relationship among the major parameters.

Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory

In this paper,the buckling behaviors of axially functionally graded and non-uniform Timoshenko beams were investigated.Based on the auxiliary function and power series,the coupled governing equations were converted into a system of linear algebraic equations.With various end conditions,the characteristic polynomial equations in the buckling loads were obtained for axially inhomogeneous beams.The lower and higher-order eigenvalues were calculated simultaneously from the multi-roots due to the fact that the derived characteristic equation was a polynomial one.The computed results were in good agreement with those analytical and numerical ones in literature.

POST-BUCKLING BEHAVIOR OF A DOUBLE-HINGED ROD UNDER SELF-WEIGHT

Post-buckling phenomena of slender rods have attracted great attention for both theoretical and engineering aspects. In this study, we explored the post-buckling behavior of a slender rod with two hinged ends under its self-weight. We first established the potential energy functional of the system, and then derived the governing differential equations according to the principle of least potential energy. We further addressed the physical meaning of the Lagrange multiplier by analyzing the force equilibrium. A computer code of shooting method was developed by using the commercial software MathCAD, which has proved efficient in computing the post- buckling configurations of the rod. We finally discussed the buckling of an oil sucker rod adopting our numerical results, which will be beneficial to the engineering design.

DISSIPATION EFFECT ON THE FLOW OVER MOUNTAINS

In the paper,the turbulent dissipation is considered in the model for studying the flow over mountains.The governing equation is a first order ordinary differential equation derived from an algebraic equation without dissipation case.The solution is sensitive to the upstream condition of dissipation.The dissipation not only reduces the strength of discontinuity but also changes the properties of the governing equation.In the paper,the qualitative characteristic features of the governing equation are discussed.The numerical results with super and sub-critical cases are also discussed in detail.The results show that the turbulent dissipation is an important factor and is not negligible.