13th International Conference on Fracture June 16-21, 2013, Beijing, China Tt =2( φn∆t δ2 t )[q+( r −q r −1) ∆n δn ]exp(− ∆n δn )exp(− ∆2 t δ2 t ) (5) 2.3. Frame element Frame element is the combination of truss element which represents axial tension and beam element that represents bending (E.g. [6]). Consider the frame element shown in Fig. 2, the element nodal Figure 2. Image of frame element displacement vector dFrame and the vector of element nodal loads FFrame are set as: ( dFrame ) T =( ui vi θi uj vj θj ) T (6) ( FFrame ) T =( Pi Qi Mi Pj Qj Mj ) T (7) As shown in Fig. 2, u, v, and θ are the x-direction displacement, y-direction displacement and deflection angle, respectively. P, Q, and Mrepresent the x-direction load, y-direction load and bending moment, respectively. The stiff equation of frame element can be expressed as: ( FFrame ) =( kFrame )( dFrame ) (8) where [kFrame] represents the element stiff matrix of the frame element of x-direction. Furthermore, if we set the length, area of cross section, Young’s modulus and moment of inertial of area as l, A, E, I, then consider the frame element that inclined at the degree of βto the x-direction. By coordinate transformation, the stiff equation of the frame element of any direction can be obtained: P∗i Q∗i M∗i P∗j Q∗j M∗j = F G H −F −G H G U V −G −U V H V S −H −V T −F −G −H F G −H −G −U −V G U −V H V T −H −V S u∗i v∗i θ∗i u∗j v∗j θ∗j (9) -3-
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