High-fidelity finite element (FE) analysis is computational demanding for parametric studies and design optimizations of composite laminates because it is time-consuming and inflexible in reconfiguration. Hence, we aim to develop rapid yet accurate 3-D FE analysis that can readily change (i) layer materials including fiber angles, (ii) the number of layers, and (iii) the stacking sequence of layers. To achieve these three features, we propose an offline-online framework hinging on static condensation (SC) integrated with port reduction (PR) and reduced basis element (RBE) methods, resulting in port-reduced static condensation (PR-SC) and port-reduced static condensation reduced basis element (PR-SCRBE) analyses. Thanks to the PR-SC and PR-SCRBE techniques, we may easily build a composite laminate using a variety of layer materials and any desired number of layers, akin to assembling Lego bricks, and swiftly analyze the constructed composite laminate. For demonstration, we assess both PR-SC and PR-SCRBE approximations using three different composite laminates with varying numbers of layers for each of three-point bending and tensile tests. Compared with FE analysis, PR-SC analysis exhibits insignificant accuracy loss in displacement and stress evaluation while obtaining meaningful computational speedup. In contrast, PR-SCRBE analysis shows moderate accuracy loss in displacement and stress evaluation while gaining considerable computational speedup. In conclusion, we recommend employing PR-SC for accuracy and PR-SCRBE for efficiency as per application requirements. The proposed two-stage framework may benefit many-query and real-time applications involving composite laminate analysis, including design optimization and virtual testing.