A recursive formulation based on corotational frame for flexible planar beams with large displacement

A forward recursive formulation based on corotational frame is proposed for flexible planar beams with large displacement.The traditional recursive formulation has been successfully used for flexible mutibody dynamics to improve the computational efficiency based on floating frame,in which the assumption of small strain and deflection is adopted.The proposed recursive formulation could be used for large displacement problems based on the corotational frame.It means that the recursive scheme is used not only for adjacent bodies but also for adjacent beam elements.The nodal relative rotation coordinates of the planar beam are used to obtain equations with minimal generalized coordinates in present formulation.The proposed formulation is different from absolute nodal coordinate formulation and the geometrically exact beam formulation in which the absolute coordinates are used.The recursive scheme and minimal set of dynamic equations lead to a high computational efficiency in numerical integration.Numerical examples are carried out to demonstrate the accuracy and validity of this formulation.For all of the examples,the results of the present formulation are in good agreement with results obtained using commercial software and the published results.Moreover,it is shown that the present formulation is more efficient than the formulation in ANSYS based on GEBF.

Large Displacement Analysis of Tapered Beam Structures

A Bernoulli-Euler beam mechanism for static analysis of large displacement,large rotation but small strain planar tapered beam structures is proposed using the Updated Lagrangian formulation and the moving coordinate method.The object beam is the tapered one whose profile is assumed to be varying linearly.From the governing differential equation of lateral deflection including second-order effects by beam-column theory,the geometric nonlinear tangent elemental stiffness matrix is derived.The nonlinear effect of the bending distortions on the axial action is considered to manifest itself as an axial change in length.The aforementioned stiffness matrix is amended,by developing the auxiliary stiffness of bowing effect.The moving coordinate method is employed for obtaining the large displacement total equilibrium equations,and the hinged-hinged moving coordinate system is constructed at the last updated configuration.The multiple load steps Newton-Raphson iteration is adopted for the solution of the nonlinear equations.The validity and efficiency of the proposed method are shown by solving various typical numerical examples.

A MODIFIED HELLINGER-REISSNER VARIATIONAL FUNCTIONAL INCLUDING ONLY TWO INDEPENDENT VARIABLES FOR LARGE DISPLACEMENT OF THIN SHALLOW SHELL

The variational functional of the Hellinger-Reissner variational principle for the large displacement problem of a thin shallow shell with an arbitrary shape is first established. Then the functional of the modified principle suitable for the finite element method is derived. In the functional only two independent variables, the deflection w and the stress function F are included. The displacement expressions in the middle surface on the boundary of the shell is also derived by means of the previous two variables.

FUNDAMENTAL EQUATIONS OF LARGE SPATIAL DEFLECTION PROBLEMS OF RODS AND ITS APPLICATION TO DRILLING ENGINEERING

The fundamental equations for analysis of a straight slender rod which deform at large deflections of order of several times of the dimension of the cross section of the rod are derived by using convecled coordinate system. In accordance with the practice of oil drilling, an effective method of three dimensional static analysis of bottom-hole assemblies is simply described. Errors in reference [8 ] are pointed out.

Large excavations and their effect on displacement of land boundaries

A study to estimate land surface movement caused by large surface excavations in sedimentary strata is presented.In stratified or jointed strata the stress relief driven movement adjacent to large excavations can be significantly larger than expected.High lateral stresses measured in Australia and other places around the world indicate that the ratio of horizontal to vertical stress has been particularly high at shallow depths.The in situ strata is in compression and during excavation,stress is relieved towards the opening causing strata movement.Large excavations such as,open cut mines or highway cuttings,can initiate an extensive horizontal slide of surface layers towards the excavation.These ground movements can be damaging to surface structures such as water storage dams and large buildings.Based on stress measurements at shallow depths in Australian coal mines the study presented here calculates and models the extent of potential ground movement along the bedding surface adjacent to large excavations and provides a new prediction tool of land movement at the excavation boundary that can benefit the geotechnical practitioners in the mining industry.

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stress-strain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.

Critical Top Tension for Static Equilibrium Configuration of A Steel Catenary Riser

This paper aims to present the critical top tension for static equilibrium configurations of a steel catenary riser（SCR） by using the finite element method. The critical top tension is the minimum top tension that can maintain the equilibrium of the SCR. If the top tension is smaller than the critical value, the equilibrium of the SCR does not exist. If the top tension is larger than the critical value, there are two possible equilibrium configurations. These two configurations exhibit the nonlinear large displacement. The configuration with the smaller displacement is stable, while the one with larger displacement is unstable. The numerical results show that the increases in the riser＇s vertical distances, horizontal offsets, riser＇s weights, internal flow velocities, and current velocities increase the critical top tensions of the SCR. In addition, the parametric studies are also performed in order to investigate the limit states for the analysis and design of the SCR.

Wavelets and Optical Flow Motion Estimation

This article describes the implementation of a simple wavelet-based optical-flow motion estimator dedicated to continuous motions such as fluid flows. The waveletrepresentation of the unknown velocity field is considered. This scale-space representation, associated to a simple gradient-based optimization algorithm, sets up a welldefined multiresolution framework for the optical flow estimation. Moreover, a verysimple closure mechanism, approaching locally the solution by high-order polynomialsis provided by truncating the wavelet basis at fine scales. Accuracy and efficiency of theproposed method is evaluated on image sequences of turbulent fluid flows.

NEURO FUZZY MODEL FOR PREDICTING THE DYNAMIC CHARACTERISTICS OF BEAMS

An adaptive neuro-fuzzy inference system （ANFIS） is introduced to predict the dynamic behavior of beams. The effects of axial forces and large displacements are considered in the analysis. A database of tests for the dynamic characteristics of beams is developed from the experimental tests. The responses of nonlinear vibration force for the single and multiple-stepped beams are calculated from the finite element method （FEM）, experimental tests and neuro-fuzzy model for comparison. The neuro-fuzzy model provides a general framework for the combination of neural networks and fuzzy logic. It is more flexible with more options of incorporating the fuzzy nature of the real-world system and is an useful estimation tool for the dynamic characteristics of beams. Therefore, ANFIS can be a useful tool for dynamic behaviour analysis of multiple-stepped beams subjected to axial loads and large displacement.

Dual reciprocity boundary element based block model for discontinuous deformation analysis

This paper presents a further development of the dual reciprocity boundary element method(DRBEM) with stepwise updating to pave the way for the introduction of boundary element mesh into the discontinuous deformation analysis(DDA). The advantage of the proposed method lies in its adoption of static fundamental solutions and reduction in the size of the governing equations by transforming the inertial term domain integrals to boundary integrals in the dynamic large displacement analysis. The unconditionally stable Newmark-β time integration method involving numerical damping to enhance the numerical stability is implemented for the dynamic analysis. In order to be coupled with the DDA to improve the deformability of the DDA block domains, a stepwise updating algorithm of the system variables is introduced. The stress updating in the analysis involved in the calculation of a domain integral and internal cells are used for the integration of the initial stress term. Several examples are used to verify the geometry-updated DRBEM model and satisfactory results have been obtained.

Multi-catenary isogeometric discretization with the sliding constraint

The purpose of this paper is to present the formulation of isogeometric dynamic analysis with frictionless sliding constraint between two catenaries.The sliding condition at the constraint point is defined employing the augmented Lagrangian method,that specifies unique degree of freedom along sliding catenary.The governing equations for the coupled system are derived in terms of Hamilton’s principle together with sliding constraint form differential algebraic equations of multi-catenary system.Recently developed isogeometric approach is employed to discretize the catenaries what enables us to define the unique degree of freedom of sliding constraint along the whole catenary and thus avoid the process of searching for the sliding point as required in some other discretization techniques,e.g.finite element method.Four numerical examples are provided to validate the proposed method and the results are assessed against the results in the literature.