Papers by Keyword: Variational Principle

Abstract: Functionally graded materials are prevalent among industries for its low weight compared to alloys. Depending upon the applications ceramic-ceramic materials can be graded to obtain novel functional combination. In a disk, yielding mainly occurs at the root, hence to overcome the yielding problem, Al₂O₃ material was used at the root and graded with different ceramics; as ceramics possess high yield strength. In composites, many methods are available to calculate effective mechanical properties and modified rule of mixture (MROM) is one of these. In MROM only single parameter, stress to strain transfer ratio needs to be identified which in present case was calculated using inverse approach i.e. by comparing Halpin-Tsai model with MROM. Variational formulation method was employed taking radial displacement field as unknown variable. The effective Young’s modulus calculated was then verified with experimental data and good agreement was seen. Further effective yield stress distribution was quantified and plotted to compare with von-Mises stress. Limit elastic speed then obtained was used to rank different ceramic-ceramic graded combinations. Limit speed defines the performance of disk and thus it was chosen as a selection parameter.

Abstract: The work considers using a multilayer elastomeric package for the vibroisolation of engineering constructions under the action of periodic vibration. The multilayer elastomeric package is located between the protected object and a vibrating base; it consists of alternating thin metallic and elastomeric layers jointed by vulcanization or gluing. The paper discusses flat rubber-metal elements of circular shapes with reinforcing steel layers and describes kinematic excitation directed flatwise. The analytical expression of the characteristics of the compression stiffness of the plane multilayered elastomeric structure is derived on the basis of the variational principle, and metallic plates-layers are assumed to be perfectly rigid. An analytical solution was confirmed by experimental data. The fitted equation for “force-displacement” was derived and used in the equation of motion on of the protected object.

Abstract: In this paper, using the variational principle of multiple two functions establishes the extremal function model of new media Internet network nodes, and the integration of Internet resources is realized by INON network node overlapping technology and P2P technology. Through the integration of Internet moral education resources in colleges, this paper carries out statistics the failure rate of computer resources, when the statistical number is 1000, the failure rate will reach the lowest, and its value is 0.2; when the statistical number is 6000, the failure rate will reach the highest, its value is 1.6. The simulation experiment has been the time curve of Internet moral education resources integration, when a number is 3000 and 4000, the required time is relatively large, and the other number required time is relatively small, which is consistent with the theory, so as to verify the reliability of multiple two variational algorithm and model.

Abstract: According to the principle of random computer nonlinear measurement, the partial differential mathematical model of computer stochastic nonlinear dynamic force signal detection is established by using multi sensor control, which can establish the computer mechanical signal detection and analysis system of the complex force detection. In order to verify the validity and reliability of the system, this paper depends on the mechanical characteristics detection of volleyball player movement process as an example, to monitor the force signal for the process of volleyball players. Through the elastic-plastic stress signal analysis, we find that when the sensor is spiral distribution, the distribution of power spectrum will be relatively stable; when the sensor is 8 shape distribution, the size of the force will be relatively stable between 18N and-18N. However, the spectrum analysis is not stable, and it agrees with the theory trend of mechanics calculation, to verify the rationality of the algorithm.

Abstract: A parametric variational principle is deduced according to the equivalent integral form of all the controlling equations and boundary conditions in elasticity, and by adjusting the parameters, all kinds of variational principles put forward past and some new variational principles can be gained, which means that the method above is more clear in concept, and more concise.

Abstract: This paper presents the series solutions in Hamiltonian form for plane sectorial domain of the nonlocal linear elasticity originally proposed by Eringen [. Based on the Hamiltonian governing equations of plane elasticity for sectorial domain, the variable separation and eigenfunction expansion techniques were employed to obtain these solutions. These solutions can be used to develop a nonlocal analytical finite element for the model I crack in nonlocal fracture mechanics.

Abstract: A microstructure-dependent Reddy beam theory (RBT) which contain only one material length scale parameter and can capture the size effect in micro-scale material unlike the classical theory is developed .using the variational principle energy the governing equation of motion is derived based on modified couple stress theory for the simply supported beam. the equations obtained are solved by Fourier series and the influence of the length scale parameter and thermal effect on static bending, vibration and buckling analysis of micro-scale Reddy beam is investigated.

Abstract: The bending deformation problem of cantilever micro-beams is solved analytically on the basis of strain gradient elasticity theory. The governing equations and boundary conditions are obtained by using Hamiltons principle. The size effect on deflections of the cantilever micro-beams is analyzed. It is found that the deflections of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

Abstract: Hamiltonian dual equation of plane transversely isotropic magnetoelectroelastic solids is derived from variational principle and mixed state Hamiltonian elementary equations are established. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate. Then the x-direction is discreted with the linear elements to obtain the state-vector governing equations, which are a set of first order differential equations in z and are solved by the analytical approach. Because present approach is analytic in z direction, there is no restriction on the thickness of plate through the use of the present element. Using the propagation matrix method, the approach can be extended to analyze the problems of magnetoelectroelastic laminated plates. Present semi-analytical method of mixed Hamiltonian element has wide application area.

Abstract: Hamiltonian system used in dynamics is introduced to formulate the three-dimensional problems of the transversely isotropic magnetoelectroelastic solids. The Hamiltonian dual equations in magnetoelectroelastic solids are developed directly from the modified Hellinger-Reissner variational principle derived from generalized Hellinger-Ressner variational principle with two classes of variables. These variables not only include such origin variables as displaces, electric potential and magnetic potential, but also include such their dual variables as lengthways stress, electric displacement and magnetic induction in the symplectic space. Similar to the Hamiltonian formulation in classic dynamics, the z coordinate is treated analogous to the time coordinate so that the method of separation of variables can be used. The governing equations are a set of first order differential equations in z, and the coefficient matrix of the differential equations is Hamiltonian in (x, y).