一 结构屈曲基本原理ppt课件

1、www.DeepWaterC浮式结构设计基础第四章第四章 构造稳性强度分析构造稳性强度分析Structural Stability Strength Analysis and Design第一节第一节 构造稳性原理构造稳性原理Structural Stability Theories闫发锁闫发锁www.DeepWaterC浮式结构设计基础Buckling Basicsn压杆的屈曲梁柱的屈曲nEuler column nPe = p2*EI/lk2n n欧拉载荷n临界载荷n前提假设n www.DeepWaterC浮式结构设计基础Load Deformation Diagram Columnsww

2、w.DeepWaterC浮式结构设计基础Non-Linear Effectsq实践梁的屈曲载荷不等于欧拉载荷的情况q梁的初始缺陷(Initial imperfection) q剩余应力Residual stressesq临界应力Critical Stresswww.DeepWaterC浮式结构设计基础The Buckling Curvesn非线性效应运用屈曲曲线来处置n屈曲曲线是建立在实验的根底上的n梁的柔度的概念nl = sqrt(fy/fe)nfy = characteristic yield stressnfe = elastic buckling stress (Euler stres

3、s)www.DeepWaterC浮式结构设计基础Buckling Curveswww.DeepWaterC浮式结构设计基础Why is a column not a plate structure?n梁的截面是由板组成的Ifn由于截面中各板的严密结合和相互作用，失效方式发生变化www.DeepWaterC浮式结构设计基础Section ClassesnClass 1 Rotation capacity of 3 with full plastic moment capacity (compact)nClass 2 Full plastic moment capacitynClass 3 Ela

4、stic moment capacity (non-compact)nClass 4 Local buckling for stress less than yield (slender)www.DeepWaterC浮式结构设计基础Column Buckling SummarynLinear elastic buckling need to be corrected for imperfections and residual stresses in order to be used in designnThe plate slenderness as expressed by the req

5、uirements to Class 3 (non-compact) will represent the limit for when a plate element will need to be checked for plate bucklingwww.DeepWaterC浮式结构设计基础Buckling of Stiffened Plate PanelsnHierarchy for stiffened panelsnIn the following the structure is assumed to be analyzed by assuming a hierarchy wher

6、e an element from the lower level is totally supported by the higher levelnThe elements are:n-Platen- stiffenern- girdern www.DeepWaterC浮式结构设计基础Classical Plate Theory均布荷载作用下各向同性板的微分方程边境条件固定边： 简支边：由w的解，得到各力分量如下44442242wwwqxxyyD 2222()xwwMDvxy 2222()ywwMDvyx 2(1)xyyxwMMDvx y 2222()xwwQDxxy 2222()ywwQD

7、yxy www.DeepWaterC浮式结构设计基础板受弯曲与拉伸或紧缩的结协作用44422242242212(2)xyxywwwwwwqNNNxxyyDxyx y 虚功原理: The principle of virtual work states that a virtual (very small) change of the internal strain energy must be offset by an identical change in external work due to the applied loads, or: U=V 构造的应变能 外力所做的功www.Dee

8、pWaterC浮式结构设计基础n弯矩Mx的应变能: n弯矩My的应变能: n扭矩Mxy的应变能： n扭矩Myx的应变能： www.DeepWaterC浮式结构设计基础The fundamental assumptions of plate theory1. The material is elastic, homogeneous, and isotropic.2. The plate is initially flat.3. The deflection of midplane is small compared with the thickness of the plate.4. The s

9、traight lines, initially normal to the middle plane before bending, remain straight and normal to the middle surface during the deformation5. The stress normal to the middle plane, z, is small and may be neglected 6. Since the displacements of a plate are small, it is assumed that the middle surface

10、 remains unstrained after bending.www.DeepWaterC浮式结构设计基础The fundamental equations of elasticity theory,xyzyzxzxyuwvxyzvuwyzxwvuzxy1(),1(),1(),yzxxyzyzzxyyzxzxxyzzxyxyEGEGEG 222222222222222222,2,2,2yxyxyyzxzxxyyzxyyzyzxzyzxyxzxzxzzyxx yxyzxy zzyy zyzxyz yxzz xzxyzx y Compatibility equationsEquilibriu

11、m equationsConstitutive equationsGeometry equationswww.DeepWaterC浮式结构设计基础Governing differential equations of plate elementGoverning differential equationsby the deflectionsBy the forcesBoundary conditions1 Clamped, or built-in, or fixed edge y =02 Simply supported edge x=a3 Free edge y=bwww.DeepWate

12、rC浮式结构设计基础Variational principles of solid mechanicsBoundaryBoundary conditionsTotal potential energy of a deformed elastic body and the loads acting on it=U+ The strain energyThe work done external forces InternalVariational principles(a) The Principle of Conservation of Energy(b)The Principle of Vi

13、rtual Work(c) The Principle of MinimumPotential Energywww.DeepWaterC浮式结构设计基础Solution of Rectangular PlatesCylindrical bending of a plate(桶形弯曲，like a beamPure bending of plates纯弯曲，Only moments22341234( )wCC xC xC xp x dxNAVIERS Method (Double series solution, 四边简支)www.DeepWaterC浮式结构设计基础Solution of Re

14、ctangular Plates (cont.)Subjected to a patch load of intensity p0=constSubjected to a concentrated force PLEVYS Solution (Single series solution, two sides simply supported and two have arbitrary supports)通解和特解Try to find the solutions of rectangular plates with different boundary conditions and loa

15、dswww.DeepWaterC浮式结构设计基础Solution of Rectangular Plates (cont.)A rectangular plate with simply supported edges is subjected to the action of a combined uniform lateral load p and uniform tension NRectangular plates under combined lateral and direct loads Governing differential equationsNAVIERS Method

16、www.DeepWaterC浮式结构设计基础Solution of Rectangular PlatesConsider a simply supported plate with sides a and b.Two plate edges are subjected to an in-plane uniform compressive force Nx=-N Rectangular plates with small initial curvatureGoverning differential equationswww.DeepWaterC浮式结构设计基础Buckling of Plate

17、sThe transition of the plate from the stable state of equilibrium to the unstable one is referred to as buckling or structural instability. In many cases, a failure of thin plate elements may be attributed to an elastic instability and not to the lack of their strength The critical load is the small

18、est load at which both the flat equilibrium configuration of the plate and slightly deflected configuration are possible.The linear buckling analysis of plates based on the following assumptions:(a) Prior to loading, a plate is ideally flat and all the applied external loads act strictly in the midd

19、le plane of the plate.(b) States of stress is described by equations of the linear plane elasticity. Any changes in the plate dimensions are neglected prior to buckling.(c) All the loads applied to the plate are dead loads; that is, they are not changed either in magnitude or in direction when the plate deforms.(d) The plate bending is described by Kirchhoffs plate bending theorywww.DeepWaterC浮式结构设计基础Bucklin