Walter D’Ambrogio and Annalisa Fregolent • also at some internal DoFs of the residual subsystemB(extended interface). By adding all internal DoF, it is: [BC]= θ1 θ3 θ4 θ5 θ8 ⎡ ⎢⎢⎢ ⎢⎣ 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 ! ! ! ! ! ! ! ! ! ! BAB C θB 1 θB 3 θB 4 θB 5 0 0 0 −1 −1 0 0 0 0 −1 0 0 0 0 −1 0 ⎤ ⎥⎥⎥ ⎥⎦ BB C By adding only one internal DoF, it is: – using θ1 as additional internal DoF: [BC]=" θ1 θ3 θ4 θ5 θ8 0 0 0 1 0 1 0 0 0 0 BAB C ! ! ! ! θB 1 θB 3 θB 4 θB 5 0 0 0 −1 −1 0 0 0 BB C # – using θ3 as additional internal DoF: [BC]=" θ1 θ3 θ4 θ5 θ8 0 0 0 1 0 0 1 0 0 0 BAB C ! ! ! ! θB 1 θB 3 θB 4 θB 5 0 0 0 −1 0 −1 0 0 BB C # – using θ4 as additional internal DoF: [BC]=" θ1 θ3 θ4 θ5 θ8 0 0 0 1 0 0 0 1 0 0 BAB C ! ! ! ! θB 1 θB 3 θB 4 θB 5 0 0 0 −1 0 0 −1 0 BB C # 4.1.2 Equilibrium In collocated approach, [BC]=[BE] in all the above cases. Except for three cases whose results will be shown afterwards, in non collocated approach equilibrium is enforced only at the coupling Dofs. Therefore: [BE]= θ1 θ3 θ4 θ5 θ8 0 0 0 1 0 BAB E | θB 1 θB 3 θB 4 θB 5 0 0 0 −1 BB E 64
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