This thesis presents new finite elements concepts to facilitate design and modelling of composite structures by exploring the Floating Node Method (FNM). It presents new element types which can be readily integrated into commercial Finite element (FE) software packages. To this end, three novel finite elements have been developed; these are polymorphic, floating connector, and hydraulic fracture elements. The polymorphic element enables a new adaptive multi-scale methodology towards more efficient and versatile damage modelling in composite structures. The element can readily morph into various element states inside one numerical analysis without resorting to remeshing. The floating connector element provides a numerical platform where combined mechanical analysis and optimization can be performed to optimize the position of a generic component without remeshing using one additional element in a FE model. The hydraulic fracture element is developed to model fluid-driven fracture problems which involve coupled multi-physics. All new element types developed are verified using relevant examples from literature and applied to relevant engineering problems.