Displacement‐based partitioned equations of motion for structures: Formulation and proof‐of‐concept applications

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Abstract
A new formulation for the displacement‐only partitioned equations of motion for linear structures is presented, which employs: the partitioned displacement, acceleration, and applied force (); the partitioned block diagonal mass and stiffness matrices (); and, the coupling projector (), yielding the partitioned coupled equations of motion: ). The key element of the proposed formulation is the coupling projector () which can be constructed with the partitioned mass matrix (), the Boolean matrix that extracts the partition boundary degrees of freedom (), and the assembly matrix () relating the assembled displacements () to the partitioned displacements () via . Potential utility of the proposed formulation is illustrated as applied to six proof‐of‐concept problems in an ideal setting: unconditionally stable explicit‐implicit transient analysis, static parallel analysis in an iterative solution mode; reduced‐order modeling (component mode synthesis); localized damage identification which can pinpoint damage locations; a new procedure for partitioned structural optimization; and, partitioned modeling of multiphysics problems. Realistic applications of the proposed formulation are presently being carried out and will be reported in separate reports.

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