DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.

RIGID FINITE ELEMENT AND ITS APPLICATIONS IN ENGINEERING

Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.

RIGID FINITE ELEMENT AND LIMIT ANALYSIS

According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the Thermo-Parameter Method(TPM)and Parametric Variational principles(PVP)are used to reduce the computational effort while maintaining the accuracy of solutions.A better solution isalso obtained in this paper.

Discrete Element with Flexible Connector for Dynamic Analysis of 3-D Beam Structures

Combined multi-body dynamics with structural dynamics, a new discrete element with flexible connector, which is applicable for 3-D beam structures, is developed in this paper. Both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off-diagonal in a general case. The zero-length rigid element is introduced to simulate the node at which multiple elements are jointed together. It may also be effective when the axes of adjacent elements are not in the same line. The examples for eigenvalue calculation show that the model is successful. It can be extended to the geometric nonlinear response analysis.

The New Rigid Element for Laminated Cylindrical Shell

Thermal effects are incorporated into developed discrete layer mechanics for two-dimensional cylindrical shells structures. Finite element equations are developed according to layerwise theory of laminated structure. Following the layerwise theory, a variable kinematic model that incorporates mechanics and thermal conditions is also presented. The new element has a field of displacement compatible with the cylindrical shell element or plate and it can be used as a rigid element for this structural element.ln the laminate model construction, adjacent layers are arranged as bonded layers. The layer has a unique constant thickness that can be different to each layer. The fiber reinforced is used and the fibers in a laminate may be oriented arbitrarily. The shear stress is adopted equal to zero because the thin thickness, on the other hand, the normal stress is maintained in order to ensure the compatibility of stress in material. The previously authors of this methods neglect the implications of thermal effects on cylindrical shells structures. Thermal effects become important when the structure has to operate in either extremely hot or cold temperature environments. These extreme conditions may severely affect the response of structure in two distinct ways： （1） induction of thermal stresses due to differences in the coefficients of thermal expansion between the various composite plies and layers and （2） temperature dependence of the elastic properties. Only a limited amount of work has been reported concerning this topic. All in all, the main contribution of this work is the consideration of this kinematic for cylindrical shells that incorporate mechanics and thermal conditions. In addition, numerical results are presented to demonstrate the capability of the current formulation to represent the behavior of cylindrical shells with these characteristics.

A NEW AEROMECHANICAL STABILITY ANALYSIS METHODOLOGY FOR COUPLED ROTOR/FUSELAGE SYSTEM OF HELICOPTERS

The aeromechanical st ability for the coupled rotor/fuselage system of helicopters in forward flight i s investigated. The periodic time-varying equations of motion are developed thr ough building a new 24DOF coupled rigid/elastic blended element based on the fle xible multibody system theory in this paper. It accounts for the effects of prec one, sweep, and the moderately large elastic deflections on the blade and elasti city of shaft and fuselage of the helicopter. The dynamic coupling between the r igid motion of blades about the flap, lag and pitch hinges of articulated rotor and moderately large elastic deflections are included. There is no restriction o n the rotation amplitudes of flap, lag and pitch in the formulation. The stabili ty of periodic solution is studied using the Floquet theory. The transition matr ix is calculated by the Newmark integration method. The aeromechanical stability of a new helicopter is studied. The results show that it is stable in the given forward flight. But the instability arises with the decrease of the bending and torsion stiffness of the shaft.

A Study of Dynamic Analysis Method for the Rigid-Flexible Coupled Bar Linkage System

In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.

Comparison of methods for vibration analysis of electrostatic precipitators

The paper presents two methods for the formulation of free vibration analysis of collecting electrodes of precipitators.The first,called the hybrid finite element method, combines the finit element method used for calculations of spring deformations with the rigid finite element method used to reflect mass and geometrical features,which is called the hybrid finite element method.As a result,a model with a diagonal mass matrix is obtained.Due to a specific geometry of the electrodes,which are long plates of complicated shapes,the second method proposed is the strip method which is a semi-analytical method.The strip method allows us to formulate the equations of motion with a considerably smaller number of generalized coordinates.Results of numerical calculations obtained by both methods are compared with those obtained using commercial software like ANSYS and ABAQUS.Good compatibility of results is achieved.

Improved Discrete Element Method for Linear and Nonlinear Dynamic Analysis of 3-D Beam Structures

Based on the combination of multi body dynamics and structural dynamics, a new model of discrete element with flexible connector is developed. It is applicable to the eigenfrequency and geometric nonlinear dynamic response analysis of three dimensional beam structures. It is pointed out that both the generalized elastic coefficient matrix of the flexible connector and the mass matrix of discrete element may be off diagonal in a general case. A special discrete element, zero length rigid element, is introduced to simulate the node at which multiple elements are jointed together. It may also be efficient when the axes of adjacent elements are not in the same line. The formulation of stiffness matrix is established while nonlinearity is taken into consideration. Given examples show that the model is successful in eigenvalue calculation and geometric nonlinear response analysis.

Finite element model validation of bridge based on structural health monitoring——Part I: Response surface-based finite element model updating

In the engineering practice, merging statistical analysis into structural evaluation and assessment is a tendency in the future. As a combination of mathematical and statistical techniques, response surface （RS） methodology has been successfully applied to design optimization, response prediction and model validation. With the aid of RS methodology, these two serial papers present a finite element （FE） model updating and validation method for bridge structures based on structural health monitoring. The key issues to implement such a model updating are discussed in this paper, such as design of experiment, parameter screening, construction of high-order polynomial response surface model, optimization methods and precision inspection of RS model. The proposed procedure is illustrated by a prestressed concrete continuous rigid-frame bridge monitored under operational conditions. The results from the updated FE model have been compared with those obtained from online health monitoring system. The real application to a full-size bridge has demonstrated that the FE model updating process is efficient and convenient. The updated FE model can relatively reflect the actual condition of Xiabaishi Bridge in the design space of parameters and can be further applied to FE model validation and damage identification.

Behavior Analysis of Biomimetic Soft Bending Actuators in Free Motion and Contact

Bioinspired Soft Bending Actuators (SBA) are increasingly being used in rehabilitation, assistant robots, and grippers. Despite many investigations on free motion modeling, understanding how these actuators interact with the environment requires more detailed research. It is caused by high compliance and nonlinearity of bioinspired soft material, which leads to serious challenges in contact conditions. In this paper, a continuous deformation analysis is presented to describe the free motion nonlinear behavior of the actuator. Based on the achieved result, this study proposes static modeling of SBA affected by a concentrated external force. For this purpose, the finite rigid element method is utilized, which is based on discretizing the actuator into smaller parts and assuming these parts as rigid serial links connected by nonlinear torsional springs. To verify the proposed model, two kinds of forces are considered to be acting on the actuator, i.e. following force and constant direction force. In addition, the effect of gravity on the actuator configuration is also investigated. The validity of the model has been demonstrated through experiments in free motion, contact conditions and the presence of gravity. It generally shows that the prediction error of robot configuration is lower than 7.5%.

Effect of sample size on the response of DEM samples with a realistic grading

This paper shows that for DEM simulations of triaxial tests using samples with a grading that is repre- sentative of a real soil, the sample size significantly influences the observed material response. Four DEM samples with identical initial states were produced： three cylindrical samples bounded by rigid wails and one bounded by a cubical periodic cell, When subjected to triaxial loading, the samples with rigid boundaries were more dilative, stiffer and reached a higher peak stress ratio than the sample enclosed by periodic boundaries. For the rigid-wall samples, dilatancy increased and stiffness decreased with increasing sample size, The periodic sample was effectively homogeneous, The void ratio increased and the contact density decreased close to the rigid walls, This heterogeneity reduced with increasing sample size. The positions of the critical state lines （CSLs） of the overall response in e-log p＇ space were sensitive to the sample size, although no difference was observed between their slopes. The critical states of the interior regions of the rigid-wall-bounded samples approached that of the homogeneous periodic sample with increasing sample size. The ultimate strength of the material at the critical state is independent of sample size.