Edited by fumihiko kimura chapman hill pp 119 131 1995

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Unformatted text preview: = Fimposed (2) ⎨ ⎩ U D [i] = U Dimposed This set of equations is called boundary conditions. In our example, boundary conditions are presented equation 3 and written using a matrix form where V vector components correspond to imposed values. Fx[1] = 0 , UDy[1] = 0, ⎡U ⎤ Fx[2] = 0, Fy[2] = Fext, [ BC ]⎢ D ⎥ = [V ] (3) ⎣F⎦ Fx[3] = 0 , UDy[3] = 0, Geometrical Study of Assembly Behaviour 305 The linear system of equation obtained while merging equations 1 and 3 is presented equation 4. ⎡ K − I ⎤ ⎡U D ⎤ ⎡ 0 ⎤ (4) ⎢ BC ⎥ ⎢ F ⎥ = ⎢V ⎥ ⎣ ⎦⎣ ⎦ ⎣ ⎦ This square system of equation composed is then solved in order to find out values of forces and displacements at each node of the mesh. 3.2. Combined approach Compared to classical calculation, boundary conditions depend on position of components after rigid movement. Figure 5 presented a simple example, where two components are separated by a seal, modelized by springs located at studied points. Both components are set in pos...
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