A Study of the Isoparametric Timoshenko Beam Element with Reduced Integration

To analyze and calculate the element characteristics matrices of space Timoshenko-beam, research work were carried out on the basis of energy variational principle. Displacement function for the space Timoshenko-beam were put forward, the expressions for element mass matrix, stiffness matrix and load array were deduced by energy functional extremum, and the explicit forms of element mass and stiffness matrices were integrated finally. Results show that the element mass and stiffness matrices computed by this method are consistent with those in related references. It has a good theoretical and practical value in the calculation for characteristics matrices of other elements.

The purpose of this paper is to present a theory that incorporates a special treatment of warping in the free vibration analysis of continuous curved thin‐walled girder bridges. The theory uses an additional degree of freedom for curved beam elements with thin‐walled sections to capture the effects of warping. The ability to use flexible piers or hinge supports with the curved‐girder warping theory is included. Formulation of both element stiffness and mass matrices is discussed. The element stiffness matrix is determined by inverting the flexibility matrix. Two example calculations using the theory are presented. The examples include a three‐span, continuously curved bridge with two flexible piers and a three‐span, continuously curved bridge with four flexible piers. The results obtained are compared to results based on other theories. Effects of warping, noncoincidence of shear center and centroid of section, flexibility of piers, and radius of curvature are shown.

Chapter 13 - Higher-order isoparametric formulation

This paper presents dynamic infinite element formulations which have been developed for soil-structure interaction analysis both in frequency and in time domains by the present authors and our colleagues during the past twenty years. Axisymmetric, 2D and 3D layered half-space soil media were considered in the developments. The displacement shape functions of the infinite elements were established using approximate expressions of analytical solutions in frequency domain to represent the characteristics of multiple waves propagating into the unbounded outer domain of the media. The shape functions were determined in terms of the excitation frequency as well as the spatial and material characteristics of the far-field soil region. Thereby the element mass and stiffness matrices become frequency dependent. As far as time domain analysis, the shape functions were further simplified to obtain closed-form frequency-dependent mass and stiffness matrices, which can analytically be transformed into time domain terms by a continuous Fourier transform. The proposed infinite elements were verified using benchmark examples, which showed that the present formulations are very effective for the soil-structure interaction analysis either in frequency or in time domain. Example applications to actual soil-structure interaction problems are also given to demonstrate the capability and versatility of the present methodology. kg]Key Words

<div class="htmlview paragraph">With highly complex structures, it is sometimes desirable to derive a dynamic model of the system from experimental vibration data. This paper presents algorithms for synthesizing the mass and stiffness matrices from experimentally derived modal data in a way which preserves the physical significance of the individual mass and stiffness elements. The synthesizing procedures allow for the incorporation of other mass and stiffness data, whether empirical or based on the analyst's insight. The mass and stiffness matrices are derived for a cantilever beam example and are compared with those obtained using earlier techniques.</div>

A novel weak form three-dimensional quadrature element solution for vibrations of elastic solids with different boundary conditions

Finite element vibration analysis of a helically wound tubular and laminated composite material beam

Element and Global Stiffness and Mass Matrices

A Petrov–Galerkin spectral element method for fractional elliptic problems

The application of the finite element method to the supersonic flutter of circular cylindrical shells subjected to internal pressure and axial compression is presented. A circular cylindrical shell element is used. The element stiffness, mass and initial stiffness matrices are given. The element aerodynamic matrix is derived based on a first order high Mach number approximation to the linear potential flow theory. The eigenvalue problem is solved by the QR algorithm. Numerical results are presented and these are compared with analytical solutions and experimental data.

Dynamic analysis of the precision compliant mechanisms considering thermal effect

In this paper, a piezolaminated stiffened shell element is formulated. This piezoelectric shellelement is a 9-noded, isoparametric, shear flexible and field-consistent element with fiveelastic degrees of freedom at each node and one electric degree of freedom per element perpiezoelectric layer. The stiffener element is a three-noded isoparametric beam element withthree degrees of freedom at each node. The effect of the stiffener is incorporated byinternally constraining the stiffener displacement fields to the relevant shell displacementfields and hence this formulation allows the positioning of the stiffener element anywherewithin the shell element along lines of natural coordinates, which gives a great flexibility inthe choice of the mesh size. This stiffened shell element is validated for staticdeflection and dynamic response with the results available in literature. The activecontrol performance of the stiffened composite plate and shell structures withdistributed piezoelectric sensors and actuators are studied using a number ofexamples. The active vibration control is carried out using the LQR optimal control.

The transfer matrix method together with a digital computer form the foundation of the dynamic analysis of rotor-bearing systems. The properties of each segment of the rotating shaft are expressed in simple matrix form and the overall dynamic behaviour is then obtained by successive multiplication of the element matrices. The main drawback associated with this method is the numerical instability in calculating natural frequencies for complex systems. The finite element method, on the other hand, uses the element stiffness and mass matrices to form the global equation of motion for the complete system. This avoids the numerical problems of the transfer matrix method at the expense of the computer memory requirements. The new method described in this paper combines the transfer matrix and finite element techniques to form a powerful algorithm for vibration analysis of rotor-bearing systems. It is shown that the accuracy improves significantly when the transfer matrix for each shaft segment is obtained from finite element techniques. The accuracy and efficiency of the hybrid method are compared with the transfer matrix method for a simply supported uniform rotating shaft where an analytical solution for the critical speeds and mode shapes is available. The method is then applied to a flexibly supported uniform shaft and a non-uniform shaft with a large disc to show the capability of the method for finding the critical speeds of complex rotor-bearing systems.

In this paper, a finite plate element for floorings consisting of a cross-laminated timber slab and a floating floor based on linear elastic behavior is presented. Both elemental mass and stiffness matrices are derived, allowing for static and dynamic analyses. For the cross-laminated timber plate, a higher order plate theory is employed, capturing the layer-wise zig-zag deformation of the plate and the stresses derived thereof accurately. It is augmented by an elastic layer representing the footfall sound insulation and an isotropic plate modeling the screed of a floating floor. In total, the finite element exhibits ten nodal degrees of freedom. Hence, larger structures can be analyzed efficiently, which is demonstrated by comparative finite element simulations with a commercial software package based on continuum elements.

The paper proposes a new computational approach using the moving element method (MEM) for simulating the dynamic responses of Mindlin plate resting on a viscoelastic foundation subjected to moving loads during abrupt braking. In this approach, the governing equations as well as the plate element mass, damping and stiffness matrices are formulated in a convected coordinate in which the origin is attached to the applied point of the moving load. Thus, the proposed method simply treats the moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. The interaction between the moving load and the plate during abrupt braking is accounted for through the vertical force and tangential wheel-pavement friction force. The effects of wheel sliding, load deceleration magnitude, friction coefficient, and plate thickness on the dynamic responses of plate are investigated.