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Introduction to the Finite Element Method
E.J. Hearn PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE, in Mechanics of Materials 2 (Third Edition), 1997 The vehicle engine mounting bracket shown in Fig. 9.39 is made from uniform steel channel section for which Young's modulus, E = 200 GN/m2. It can be assumed for both channels that the relevant second moment of area, I = 2 × 10–8 m4 and cross-sectional area, A = 4 x 10–4 m2. The bracket can be idealised as two beams, the common junction of which can be assumed to be infinitely stiff and the other ends to be fully restrained. Using the displacement based finite element method, and representing the constituent members as simple beam elements:
(a)
assemble the necessary terms in the structural stiffness matrix;
(b)
hence, determine for the condition shown in Fig. 9.39 (i) the nodal displacements with respect to the global coordinates, and (ii) the combined axial and bending extreme fibre stresses at the built-in ends and at the common junction.