TAILIEUCHUNG - The elastoplastic problem of the half-space with a hole subjected to axially symmetric loading

The elastoplastic problem of the half-space with a hole subjected to axially symmetric loading considered in this paper is based on the elastoplastic deformation process theory. Solution of t his problem is carried out by using the modified elastic solution method and the finite element method. Some results of numerical calculation are presented here to give the picture of plastic domains enlarging in the body and t he obtained displacements on the free boundary of the half-space. | Vietnam J ournal of Mechanics, VAST, Vol. 27, No. 4 (2005), pp. 245 - 255 THE ELASTOPLASTIC PROBLEM OF THE HALF-SPACE WITH A HOLE SUBJECTED TO AXIALLY SYMMETRIC LOADING Vu Do LONG Vietnam National University, Hanoi elastoplastic problem of the half-space with a hole subjected to axially symmetric load ing considered in t his paper is based on the elastoplastic deformation process theory. Solution of t his problem is carried out by using the modified elastic solution method and the finite element method. Some results of numerical calculation are presented here to give the picture of plastic doma ins enlarging in the body a nd t he obtained displacements on the free boundary of the ha lf-space. 1. GOVERNING EQUATIONS Let 's consider an elastoplastic half-space with a hole subjected to axially symmetric loading, the strain state of which is determined by Cauchy relation u EO = - ; r 8u /rz = 8v az + Br , /rO = /zO = O; where u = ur(r, z), v = Uz(r , z) and uo = 0 are displacement components. The stress-strain relation for elastic state can be expressed as follows: >. >. ~1 [::1 >. + 2µ = [D]{c}, 0 µ ( ) /rz where [DJ -the matrix of elastic constants >. - Ev - (1 + v)( l - 2v) ' E µ = G = 2(1 + v) Stress and strain intensity are determined in the form Eu = j~eijeij = v; V( Er - Ez) 2 + (Ez - Eo) 2 + (Eo - Er ) 2 + (3/2)1';~ , () 246 Vu Do Long and the arc-length of the strain trajectory t s j J~ = () dt . 0 For a plastic problem we use the elastoplastic deformation process theory [1] () dO"ijkl = DijkldEkl' or in matrix form {dO"} = dO"r dO"z ] dO"B rD1 D5 Dg D13 = rdTrz D2 D5 D10 D14 D3 D1 Du D15 4 D Ds ] D12 D 16 rdc:z dc:r] dc:B = [D]d{dc} , () drrz where [D]d is matrix of stress-strain relation of elastic-plastic behaviour, Di can be written as following D1=.\+2G -H1 ; D2 = .\-H2; D5 = D2; D5=.\ + 2G-H5 ; Dg = D3; D10 = D1; D13 = D4; D3 = .\-H3; D1=.\-H1; Du

• Cơ khí - Chế tạo máy
• Vietnam Journal of Mechanics
• The elastoplastic problem
• The half space with a hole subjected
• Axially symmetric loading
• The half space
• The modified elastic solution method
• 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