Carl T.F. Ross.'s Finite element techniques in structural mechanics PDF

By Carl T.F. Ross.

ISBN-10: 189856325X

ISBN-13: 9781898563259

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3 [K] = structural stiffness matrix Sec. 5. Determine the resulting nodal deflections. 5 2 2 m 2. O-Sra £»T EEL. Figure 2 ^ - Two element compound bar. 15). 16). 19) 3 The vector of external loads {qp} is obtained by making the first nodal load equal to the value of the nodal toad in the direction of the first free displacement, namely this is zero in this case. The second external load is obtained by making this load equation to the nodal load that corresponds to the second free displacement, namely u,; this is 10 kN in this case.

1 Structural Stiffness Matrix [K] In the finite element method, the structure is assumed to consist of a large number of elements and the normal process is to obtain the stiffness matrix of each element in turn and then to mathematically join together these elements to form the stiffness matrix of the entire structure. 4. 4 - Two element structure. 2 First let us determine the elemental stiffness matrix of each element in turn. 12) The displacements u „ u and u are not part of the stiffness matrices, but are included to show which part of the elemental stiffness matrices that corresponds to these displacements.

6, which lies at an angle α to the horizontal axis. 6 - Rod element in global axes. 6, the global axes are x° and y°, and the forces acting in these directions are X° and Y°, respectively. The displacements corresponding to x° and y° are u" and v°, respectively. Similarly, χ and y are the local axes, and X and Y are the forces corresponding to these directions. Also u and ν are the local displacements corresponding to χ and y, respectively. Now, as the rod only has axial stiffness, Y, = Yj = 0, and AE , , — (u, - up & x i = T χ, - A?

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Finite element techniques in structural mechanics by Carl T.F. Ross.

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