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

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 ((Figure presented.)); the partitioned block diagonal mass and stiffness matrices ((Figure presented.)); and, the coupling projector ((Figure presented.)), yielding the partitioned coupled equations of motion: (Figure presented.)). The key element of the proposed formulation is the coupling projector ((Figure presented.)) which can be constructed with the partitioned mass matrix ((Figure presented.)), the Boolean matrix that extracts the partition boundary degrees of freedom ((Figure presented.)), and the assembly matrix ((Figure presented.)) relating the assembled displacements ((Figure presented.)) to the partitioned displacements ((Figure presented.)) via (Figure presented.). 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.