Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

INCOMPATIBLE CURVED QUADRILATERAL PLATE BENDING ELEMENT WITH 12-DEGREES OF FREEDOM

This paper presents a new curved quadrilateral plate element with 12-degree freedom by the exact element method[1]. The method can be used to arbitrary non-positive and positive definite partial differential equations without variation principle. Using this method, the compatibility conditions between element can be treated very easily, if displacements and stress resultants are continuous at nodes between elements. The displacements and stress resultants obtained by the present method can converge to exact solution and have the second order convergence speed. Numerical examples are given at the end of this paper, which show the excellent precision and efficiency of the new element.

THE CURVED BEAM ELEMENT AND ITS CONVERGENCE RATE

The quasi-conforming element of the curved beam and shallow curved beam is given in this paper. Numerical examples illustrate that the quasi-conforming elements of the curved beam and shallow curved beam which is used to approximate the curved beam have better accuracy than the straight beam clement. The curved beam element constructed by displacement method can not satisfy rigid body motion condition and the very fine grids have to be used in order to satisfy rigid body motion condition approxtmately.In this paper it is proved that the straight beam element and the quasi-conforming element of the curved beam and shallow curved beam, when element size is reduced infinitely, have convergence rate with the same order O(l2) and when regular elements are used. I is the element length.

3D mixed finite elements for curved,flat piezoelectric structures

The Tangential-Displacement Normal-Normal-Stress(TDNNS)method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials.It uses tangential components of the displacement and normal components of the normal stress vector as degrees of freedom for elasticity.For the electric field,the electric potential is used.The TDNNS method has been shown to provide elements which do not suffer from shear locking.Therefore thin structures(e.g.piezoelectric patch actuators)can be modeled efficiently.Hexahedral and prismatic elements of arbitrary polynomial order are provided in the current contribution.We show that these elements can be used to discretize curved,shelllike geometries by curved elements of high aspect ratio.The order of geometry approximation can be chosen independently from the polynomial order of the shape functions.We present two examples of curved geometries,a circular patch actuator and a radially polarized piezoelectric semi-cylinder.Simulation results of the TDNNS method are compared to results gained in ABAQUS.We obtain good results for displacements and electric potential as well as for stresses,strains and electric field when using only one element in thickness direction.

A second order isoparametric finite element method for elliptic interface problems

A second order isoparametric finite element method （IPFEM） is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.

Local buckling of thin plate on tensionless elastic foundations under interactive uniaxial compression and shear

This paper uses a mathematical method to develop an analytical solution to the local buckling behaviour of long rectangular plates resting on tensionless elastic Winkler foundations and under combined uniform longitudinal uniaxial compressive and uniform in-plane shear loads. Fitted formulas are derived for plates with clamped edges and simplified supported edges. Two examples are given to demonstrate the application of the current method： one is a plate on tensionless spring foundations and the other is the contact between the steel sheet and elastic solid foundation. Finite element （FE） analysis is also conducted to validate the analytical results. Good agreement is obtained between the current method and FE analysis.

Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

ALGEBRAIC-GEOMETRY FOUNDATION FOR CONSTRUCTING SMOOTH INTERPOLANTS ON CURVED SIDES ELEMENT

The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.