IntroductionS 1-2 The Several Basic Concepts of the Elasticity1.External forceIt can be divided into the force of volume and plane accordingto the different distribution of the external force, which are calledbody force and surface force, respectively(1).Body force(a) Definition: The force acting on eachinternal particle of body or structuralmembers is so called body force. ForZ40example, gravity and inertia force. It isAVshown in Fig.1-2.(b) Property: Body force is different0from the different locations; theydistribution of the body force iscontinuous.Fig.1-2x6
6 §1-2 The Several Basic Concepts of the Elasticity It can be divided into the force of volume and plane according to the different distribution of the external force, which are called body force and surface force, respectively. (b) Property: Body force is different from the different locations; the distribution of the body force is continuous. 1.External force (1).Body force (a) Definition: The force acting on each internal particle of body or structural members is so called body force. For example, gravity and inertia force. It is shown in Fig.1-2. z x y △V O X P Y Q F Fig.1-2 Z
Introduction(c） Gather degree:The average gather degree of volumetric force:AVAOThe gather degree of volumetric force at point P: F = limAVAV->0The direction of F is the limited one of △Q(d) The components of the body force:The force of F is resolved along with the threecoordinates, which will get the three components ofF= Xi +Yi+Zkstraight intersection:X,Y,Z are called the components of the body force atpoint P. Plus sign and negative sign are separatelydetermined by the direction of the components, and its unitis [Force][Length]-37
7 （c）Gather degree： （d）The components of the body force： The force of F is resolved along with the three coordinates, which will get the three components of straight intersection: F Xi Yj Zk = + + X,Y,Z are called the components of the body force at point P. Plus sign and negative sign are separately determined by the direction of the components, and its unit is [Force][Length]-3 . The average gather degree of volumetric force: . V Q The gather degree of volumetric force at point P: . V Q F V = → lim 0 The direction of F is the limited one of . Q
Introduction(2). Surface force(a) Definition: Surface force is distributed in the surface of theobject. For instance, liquid pressure and contact forceIt is shown in Fig.1-3.(b) Property: In general, surface force is the function of thelocated coordinates of the point in the surface of the object(c) Gather degree of surface force: The average gather degreeof the surface force on △Sis: 4ASAOThe gather degree of the surfacezforce at P:FASAQF = limAS->0 △SPX(d) The components of surface force)The components of surface forceFig.1-3areX , Y, Z and the dimension is[Force][Length]-2.x8
8 (2). Surface force (c) Gather degree of surface force: The average gather degree of the surface force on is: . S S Q The gather degree of the surface force at P: S Q F S = →0 lim (d) The components of surface force: The components of surface force are , , , and the dimension is [Force][Length]-2 . X Y Z x y z P △S X Y Z F Q Fig.1-3 (b) Property: In general, surface force is the function of the located coordinates of the point in the surface of the object. (a) Definition: Surface force is distributed in the surface of the object. For instance, liquid pressure and contact force . It is shown in Fig.1-3. Q