工程有限元分析英文课件：Revolution Body.ppt

Stress Analysis of Axisymmetric Problems 1 1 Stress Analysis of Axisymmetric Problems 2 2 Stress Analysis of Axisymmetric Problems 3 3•Some of examples in engineering application Solid flywheel The Rotor of Turbocharger (整体飞轮整体飞轮) (涡轮增压器涡轮增压器转子转子)The stress analysis for axisymmetric solids(轴对称体) under axisymmetric loading is of quite interest in engineering. Stress Analysis of Axisymmetric Problems 4 4•For the problem to be axisymmetric, it must satisfy with (1) geometry and material being axisymmetric; (2) loading condition being axisymmetric; (3) support condition (BC) being axisymmetric. The response of a structure (结构响应结构响应) is also axisymmetric (radially symmetric,径向对称径向对称). Definition of Axisymmetric ProblemsThis is meant that the field variables(场变量场变量) in structural analysis are axisymmetric with respect to the axis of revolution. Stress Analysis of Axisymmetric Problems 5 5Cylindrical Polar Coordinate System（（圆柱极坐柱极坐标系）系）  Stress Analysis of Axisymmetric Problems 6 6 Stress Analysis of Axisymmetric Problems 7 Stress Analysis of Axisymmetric Problems 8 8（喷嘴出口锥管）（喷嘴出口锥管） Stress Analysis of Axisymmetric Problems 9 9m (rm, zm)j(rj, zj)i(ri, zi) Stress Analysis of Axisymmetric Problems 10Relevant Nodal Displacement Components Stress Analysis of Axisymmetric Problems 11 Stress Analysis of Axisymmetric Problems 12Turbine Disc（涡轮盘涡轮盘） modelled by a collection of triangular ring elements (环状单元的集成环状单元的集成)  Stress Analysis of Axisymmetric Problems 13Axisymmetric elements can be generated by rotating following planar shape about an axis of revolution: Axisymmetric Ring Elements Stress Analysis of Axisymmetric Problems 144.1 Interpolation Functions Stress Analysis of Axisymmetric Problems 15u - the displacement component in r (radial) directionw - the displacement component in z (axial) direction  Stress Analysis of Axisymmetric Problems 16 Stress Analysis of Axisymmetric Problems 17 Stress Analysis of Axisymmetric Problems 18ijmTriangular Segment Area Stress Analysis of Axisymmetric Problems 19Area Coordinates for triangle ijmThe displacement model(位移模式位移模式) can be expressed in terms of the area coordinates.  Stress Analysis of Axisymmetric Problems 20 Stress Analysis of Axisymmetric Problems 214.2 Strain-Displacement Relations  Stress Analysis of Axisymmetric Problems 22 Stress Analysis of Axisymmetric Problems 23 Stress Analysis of Axisymmetric Problems 24Strain - Displacement Transformation Stress Analysis of Axisymmetric Problems 25Strain Matrix  Stress Analysis of Axisymmetric Problems 264.3 Stress - Strain Relations Material Compliance Matrix (材料柔度矩阵材料柔度矩阵) Stress Analysis of Axisymmetric Problems 27Constitutive RelationsMaterial Stiffness Matrix Stress Analysis of Axisymmetric Problems 28Constitutive Relations Stress Analysis of Axisymmetric Problems 29Stress Matrix Stress Analysis of Axisymmetric Problems 30 Stress Analysis of Axisymmetric Problems 31 Approximate Procedure(近似解法近似解法) 将单元近似地当作常应变（常应力）单元来处理。

将单元近似地当作常应变（常应力）单元来处理 Stress Analysis of Axisymmetric Problems 32 Stress Analysis of Axisymmetric Problems 33 Stress Analysis of Axisymmetric Problems 344. 4 Element Stiffness Matrices  Stress Analysis of Axisymmetric Problems 35Element Stiffness Matrix Stress Analysis of Axisymmetric Problems 36Element Stiffness Matrix Stress Analysis of Axisymmetric Problems 37Element Stiffness Matrix Stress Analysis of Axisymmetric Problems 38Approximate Procedure Stress Analysis of Axisymmetric Problems 39Element Stiffness Matrix Stress Analysis of Axisymmetric Problems 404.5 Element Equivalent Nodal Force Vector  Stress Analysis of Axisymmetric Problems 41 Stress Analysis of Axisymmetric Problems 42Nodal Force Vector Equivalent to Body Forces (体积力的等效节点力体积力的等效节点力) Stress Analysis of Axisymmetric Problems 43Similar to Eq (2.57)Nodal Force Vector Equivalent to Body Forces  Stress Analysis of Axisymmetric Problems 44Nodal Force Vector Equivalent to Body Forces  Stress Analysis of Axisymmetric Problems 45Nodal Force Vector Equivalent to Surface Forces (表面力的等效节点力表面力的等效节点力) Stress Analysis of Axisymmetric Problems 46Nodal Force Vector Equivalent to Surface Forces  Stress Analysis of Axisymmetric Problems 47 Stress Analysis of Axisymmetric Problems 48 Stress Analysis of Axisymmetric Problems 49 Stress Analysis of Axisymmetric Problems 50 Stress Analysis of Axisymmetric Problems 51(如果单元离开对称轴较远，可以认为将如果单元离开对称轴较远，可以认为将1/3的自重移置到每个节点上。

的自重移置到每个节点上) Stress Analysis of Axisymmetric Problems 52 Stress Analysis of Axisymmetric Problems 53 Stress Analysis of Axisymmetric Problems 54 Stress Analysis of Axisymmetric Problems 55 Stress Analysis of Axisymmetric Problems 56 Stress Analysis of Axisymmetric Problems 57 Stress Analysis of Axisymmetric Problems 58 Stress Analysis of Axisymmetric Problems 59 Stress Analysis of Axisymmetric Problems 60 Stress Analysis of Axisymmetric Problems 61 Stress Analysis of Axisymmetric Problems 624.6 Four - Node Rectangular Ring Element  Stress Analysis of Axisymmetric Problems 63 Stress Analysis of Axisymmetric Problems 64 Stress Analysis of Axisymmetric Problems 65 Stress Analysis of Axisymmetric Problems 66 Stress Analysis of Axisymmetric Problems 67 Stress Analysis of Axisymmetric Problems 68 Stress Analysis of Axisymmetric Problems 69 Stress Analysis of Axisymmetric Problems 70Stresses in a Sphere under Internal Pressure (a) triangular mesh – centroidal values; (b) triangular mesh – nodal averages; (c) quadrilateral mesh obtained by averaging adjacent trianglesNumerical Examples Stress Analysis of Axisymmetric Problems 71Displacements of internal and external surfaces of sphere  Stress Analysis of Axisymmetric Problems 72Damage-displacement field after ( 20 ) elements failed FEM modelling for Screw and Nut (螺钉螺钉和螺母和螺母) Made of Steel-30CrMnSiNi2A  Stress Analysis of Axisymmetric Problems 73Stress-displacement field after ( 20 ) elements failed Screw and Nut Made of Steel-30CrMnSiNi2A  Stress Analysis of Axisymmetric Problems 74 Stress Analysis of Axisymmetric Problems 75Axially symmetric Elements  Stress Analysis of Axisymmetric Problems 76Axially symmetric Elements Fig.1 Stress Analysis of Axisymmetric Problems 77Axially symmetric Elements  Stress Analysis of Axisymmetric Problems 78 Stress Analysis of Axisymmetric Problems 79。