TAILIEUCHUNG - Principle of compatibility and non-generalised coordinates

In the article the author derived the theoretical basis as well as numerical algorithms concerning the combination of nongeneralised coordinates with the principle of compatibility. Some comparisons of the technique under consideration and usual technique using Lagrange multipliers are discussed. Some examples are shown for illustration. The case of contact of moving disc on the surface is given in detail | Vietnam Journal of Mechanics, Vol. 27, No. 2 (2005 ), pp. 74 - 85 PRINCIPLE OF COMPATIBILITY AND NON-GENERALISED COORDINATES DINH VAN PHONG Hanoi University of Technology Abstract. The contribution is devoted to using so-called non-generalised coordinates for deriving the system of equations of motion. Differently from common techniques for constrained mechanical systems the principle of compatibility is chosen as the tool. This takes the advantage in the possibility for extension to systems with nonideal constraints, however, the special treatment is needed. In the article the author derived the theoretical basis as well as numerical algorithms concerning the combination of nongeneralised coordinates with the principle of compatibility. Some comparisons of the technique under consideration and usual technique using Lagrange multipliers are discussed. Some examples are shown for illustration. The case of contact of moving disc on the surface is given in detail 1. INTRODUCTION As known the configuration and the motion of mechanical systems are described by a set of coordinates. Various coordinate systems can be used, therefore the sets of coordinates and equations of motion are different to each other. Commonly we can call them, regardless to the physical meaning, as generalised coordinates and use them for deriving equations of motion. Since generalised coordinates describe the configuration of mechanical system, each coordinate is related to the mass properties of the system. For each coordinate we dispose of one equation of motion in the form of a differential equation of second order. Therefore, if the system is determined by n generalised coordinates we get the system of n differential equations. Obviously, if these coordinates are not independent, the constraint equations are added to the existing system of differential equations. The system is called the constrained mechanical system, see . [1], [4], [9], [17], [24], [27] etc. In engineering .

• Vật lý
• Vietnam Journal of Mechanics
• Principle of compatibility and non generalised coordinates
• Numerical algorithms concerning
• The technique under consideration
• The combination of nongeneralised coordinates
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
• Languages Gibian and special operators
• The application FEM
• Betts miller janjic convective parameterization scheme
• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
• The gulf of Tonkin
• The kinetic energy distribution
• Duality in the analysis of responses to nonlinear systems
• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
• Aerodynamics of a wing in surface effect ship
• Theory and experiment
• Wing in surface effect ship
• The aerodynamic characteristics
• The Institute of Mechanics
• The error estimate
• The convergence rate for h
• p refinement
• The finite element analysis
• Three dimensional elastostatic mechanics problems
• Some initial experimental results
• Free water layer formation in horizontal pipes
• Water layer formation
• Hanoi Institute of Mechanics
• Bending vibration of beam elements under moving loads
• Considering vehicle braking forces
• Fluctuations of structures
• Beam elements according
• Continuous element for vibration analysis
• Thick shells of revolution
• Continous Element Method
• Finite element solutions
• Natural frequencies and harmonic responses
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• Buckling analysis of simply supported composite laminates subjected
• In plane compression load
• A novel mesh ffree method
• Alternative numerical technique
• Mesh free method
• A three story building
• Hedge algebras based fuzzy controller
• The structural system
• The El Centro earthquake
• Three story building against earthquake
• Laminar separation phenomenon combining with numerical calculations
• The turbulent separation
• The laminar separation
• Experimental study on mechanical properties
• Three phase polymer composite reinforced
• Glass fibers and titanium oxide particles
• Polymer composite reinforced
• Three phase composite
• Dynamic characteristics of elastically supported beam subjected
• A compressive axial force and a moving load
• The implicit Newmark method
• The Galerkin finite element method
• The axial force
• Eccentrically stiffened functionally graded plates and shallow shells
• Von Karman Donnell sense
• The formulation of governing equations
• The classical shell theory
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Evaluating structural safety based on fuzzy set theory
• Evaluating structural safety
• The fuzzy reliability
• Simple beam structure