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

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 (d, d, f); the partitioned block diagonalmass and stiffness matrices (M, K); and, the coupling projector (P-d), yielding the partitioned coupled equations of motion: Md =P-d(f - Kd). The key element of the proposed formulation is the coupling projector (P-d) which can be constructed with the partitioned mass matrix (M), the Boolean matrix that extracts the partition boundary degrees of freedom (B), and the assembly matrix (L-g) relating the assembled displacements (d(g)) to the partitioned displacements (d) via (d = L(g)d(g)). 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.