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 (d,d¨,f$$ \mathbf{d},\ddot{\mathbf{d}},\mathbf{f} $$); the partitioned block diagonal mass and stiffness matrices (M,K$$ \mathbf{M},\mathbf{K} $$); and, the coupling projector (풫d), yielding the partitioned coupled equations of motion: Md¨=풫d(f−Kd). The key element of the proposed formulation is the coupling projector (풫d) which can be constructed with the partitioned mass matrix (M$$ \mathbf{M} $$), the Boolean matrix that extracts the partition boundary degrees of freedom (B$$ \mathbf{B} $$), and the assembly matrix (Lg$$ {\mathbf{L}}_g $$) relating the assembled displacements (dg$$ {\mathbf{d}}_g $$) to the partitioned displacements (d$$ \mathbf{d} $$) via (d=Lgdg)$$ \left(\mathbf{d}={\mathbf{L}}_g{\mathbf{d}}_g\right) $$. 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. [ABSTRACT FROM AUTHOR]