ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL I： GENERALIZED VARIATIONAL THEORETICAL MODELING

Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which are coincident with the ones in literature.     

ANALYSIS ON THE MAGNETO-ELASTIC-PLASTIC BUCKLING/SNAPPING OF CANTILEVER RECTANGULAR FERROMAGNETIC PLATES

An analysis of buckling/snapping and bending behaviors of magneto-elastic-plastic interaction and coupling for cantilever rectangular soft ferromagnetic plates is presented.Based on the expression of magnetic force from the variational principle of ferromagnetic plates,the buckling and bending theory of thin plates,the Mises yield criterion and the increment theory for plastic deformation,we establish a numerical code to quantitatively simulate the behaviors of the nonlinearly multi-fields coupling problems by the finite element method.Along with the phenom- ena of buckling/snapping and bending,or the characteristic curve of deflection versus magnitude of applied magnetic fields being numerically displayed,the critical loads of buckling/snapping, and the influences of plastic deformation and the width of plate on these critical loads,the plastic regions expanding with the magnitude of applied magnetic field,as well as the evolvement of deflection configuration of the plate are numerically obtained in a case study.     

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface, in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell, by means of expanding field quantities as Legendre series, a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate, which has a satisfactory computational effectiveness and precision for an arbitrary frequency range. It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed. It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell, and give the coupling system a very rich resonance frequency spectrum. Moreover, the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.     

MORE GENERALIZED HYBRID VARIATIONAL PRINCIPLE AND CORRESPONDING FINITE ELEMENT MODEL

According to recent studies of the generalized variational principle by Professor ChienWeizang,the more generalized hybrid variational principle for finite element method isgiven,from which a new kind of the generalized hybrid element model is etablished.Using the thin plate bending element with varying thickness as an example,wecompare various hybrid elements based on different generalized variational principles.     

A potential-hybrid/mixed finite element scheme for analysis of plates and cylindrical shells

Based on the potential-hybrid/mixed finite element scheme,4-node quadrilateralplate-bending elements MP4,MP4a and cylindrical shell element MCS4 are derived with,the inclusion of splitting rotations.All these elements demonstrate favorable convergencebehavior over the existing counterparts,free from spurious kinematic modes and do notexhibit locking phenomenon in thin plate/shell limit.Inter-connections between the existingmodified variational functionals for the use of formulating C~0-and C~1-continuous elementsare also indicated.Important particularizations of the present scheme include Prathap’sconsistent field formulation,the RIT/SRIT-compatible displacement model and so on.     

Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material(FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching–bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-ofvariables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

STRESS ANALYSIS OF HYPERBOLIC SHELLS OF REVOLUTION WITH NON-AXISYMMETRICAL GEOMETRIC IMPERFECTIONS

In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, anapproximate method based on simulating the effect of imperfections by the application offictitious normal pressure loading on the perfect shell is investigated.In the analysis of ashell of revolution with a bulge-type imperfection under non-axisymmetric loads,anefficient algorithm of applying the method is developed;the effect of individual curvatureerrors on stress resultants and couples are separately considered,while the interactionsamong various curvature errors are properly treated in the analysis by an iterativeprocedure. This algorithm avoids repeated analyses for non-axisymmetric loads and maybe implemented with a purely axisymmetric analysis capability.A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under deadload and wind load conditions by the equivalent load method.A direct analysis of theimperfect shell is also made by a specialized finite element program. Through numericalstudie     

NUMERICAL PREDICTION OF PROCESS-INDUCED RESIDUAL STRESSES IN GLASS BULB PANEL

A numerical simulation model for predicting residual stresses which arise during the solidification process of pressed glass bulb panel was developed. The solidification of a molten layer of glass between cooled parallel plates was used to model the mechanics of the buildup of residual stresses in the forming process. A thermorheologically simple thermoviscoelastic model was assumed for the material. The finite element method employed was based on the theory of shells as an assembly of flat elements. This approach calculates residual stresses layer by layer like a truly three-dimensional calculation, which is well suited for thin pressed products of complex shape. An experimental comparison was employed to verify the proposed models and methods.     

Formulations of a hydromechanical interface element

A hydromechanical interface element is proposed for the consideration of the hydraulic-mechanical coupling effect along the interface.The fully coupled governing equations and the relevant finite element formulations are derived in detail for the interface element.All the involved matrices are of the same form as those of a solid element,which makes the incorporation of the model into a finite element program straightforward.Three examples are then numerically simulated using the interface element.Reasonable results confirm the correctness of the proposed model and motivate its application in hydromechanical contact problems in the future.     

Investigation of temperature effect on stress of flexspline

The effect of temperature loading on the stress of a flexspline is investigated. Based on the geometric and mechanical characteristics of the harmonic gear flexspline, a circular thin shell model is presented in this paper. The theoretical solution for the flexspline under different displacement loads and different temperature fields is derived. Meanwhile, an impact factor formula, which reflects the effect of the temperatures of the inner and outer surfaces of the flexspline on the stress of the flexspline, is presented. Finally, numerical calculations by the finite element method （FEM） are adopted to verify the corresponding conclusions.     

New discrete element models for elastoplastic problems

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.     

A FINITE ELEMENT METHOD FOR DIELECTRIC ELASTOMER TRANSDUCERS

We present a finite element method for dielectric elastomer(DE) transducers based on the nonlinear field theory of DE.The method is implemented in the commercial finite element software ABAQUS,which provides a large library functions to describe finite elasticity.This method can be used to solve electromechanical coupling problems of DE transducers with complex configurations and under inhomogeneous deformation.     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

Base force element method of complementary energy principle for large rotation problems

Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work. With the reservation of the axial nonlinear strain, there are more coupling terms for axial and transverse deformations. The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind. Time responses are conducted to compare the proposed model with other previous models. The stretching deforma...     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root-mean-square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander’s nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.     

A PENALTY-HYBRID FINITE ELEMENT ANALYSIS OF STOKES FLOW

A type of penalty-hybrid variational principle is suggested for the analysis ofStokesian flow.On such a basis,a finite element model is formulated featuring,amongothers,a priori satisfaction of the deviatoric stress and hydrostatic pressure on linearmomentum balance equations.Also in the present scheme the hydrostatic pressure issuccessfully eliminated at the element level,leaving only nodal velocities as solutionunknowns.A series of4-node and8-node quadrilateral elements are derived and examined.Numerical examples demonstrating their characteristic behaviors are also included.