Assembly&thermal

Assembly&thermal - Assembly of the Global Stiffness...

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1 Assembly of the Global Stiffness Matrix A structure is modelled with many finite elements each having its own element stiffness matrix defined with respect to its own axis system (local axes). Element stiffness matrices are first transformed to global axes by pre- and post-multiplying each with a coordinate transformation matrix. Entries of such a matrix contain sines and cosines of the angles between the respective local axes and the global axes. The transformed element stiffness matrices are then assembled together to form one big stiffness matrix for the structure (global stiffness matrix) .
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2 Assembly of the Global Stiffness Matrix : Example Given a cantilever beam with a distributed transverse force (a) The loading is converted to equivalent nodal forces and moments in a two-element model of the beam (b) The two elements (c) comprising have Node 2 in common. In the assembly, because no axis change is required, element stiffness matrix entries corresponding to common nodal dof are added directly. L T q(x) (a) 2@L=L T M e1 M e3 M e2 Q 1 Q 3 Q 2 (b) x 1 (c) θ 1 θ 2 v 1 v 2 x 2 v 2 v 3 θ 2 θ 3
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3 Global Stiffness Matrix for the Two-Element Model The two elements have the same 4x4 stiffness matrix. Upon
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Assembly&thermal - Assembly of the Global Stiffness...

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