Elastic multi-structures (EMS) are usually composed of elastic substructures of the same or different dimensions, which are coupled together by some junction conditions (rigid or contact connection). They are widely used in the fields of aviation, aerospace, civil engineering, mechanical manufacturing, etc. The remarkable features of elastic multi-structure problems include that (1) the geometric domains occupied by individual elastic members may have different dimensions; (2) the PDEs governing the deformation over individual elastic members are heterogenous; (3) the interface conditions among different elastic members are heterogeneous. Therefore, Prof. Ciarlet mentioned in his monograph “Mathematical Elasticity II” that “A challenging program consists in numerically approximating the mathematical models of elastic multi-structures that comprise “many” substructure.” In this talk, we will give a brief survey on FEMs and DDMs on EMS problems in the past ten years and focus on a nonoverlapping DDM for elastic body-plate problems.

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