Abstract interpretation provides a general framework to generate program invariants automatically. However, most existing numerical abstract domains under this framework can only express constraint sets that are geometrically convex. Therefore, using convex abstract domains to analyze special program structures involving disjunctive semantics (whose constraint sets are non-convex) may lead to imprecise results. This paper presents a novel approach based on loop decomposition and deduction to improve invariant generation for loop structures with explicit and implicit disjunctive semantics. This approach can alleviate the problem of great semantic loss during abstract interpretation of loop structures with disjunctive semantics. Compared with existing approaches, experimental results show that the presented approach can generate more precise invariants for loop structures involving disjunctive semantics, which is also helpful for reasoning about certain security properties.