Warp knitted (WK) fabrics are typically three-dimensional (3D) structures, and their design is strongly dependent on the structural simulation. Most of the existing simulation methods are only capable of two-dimensional (2D) modelling, which lacks of perceptual realism and cannot show design defects, making it hard for a manufacturer to produce the required fabrics. The few existing methods capable of 3D structural simulation are computationally demanding and therefore can only run on powerful computers, which makes it hard to utilize online platforms (e.g. clouds, mobile devices, etc.) for simulation and design communication. To fill the gap, a novel, lightweight and agile geometric representation of warp knitting loops is proposed to establish a new framework of 3D simulation of complex warp knitted structures. Further, the new representation has great simplicity, flexibility and versatility and is used to build high-level models in representing the 3D structures of warp knitted fabrics with complex topologies. Simulations of a variety of warp knitted fabrics are presented to demonstrate the capacity and generalizability of this newly proposed methodology. It has also been used in the virtual design of warp knitted fabrics in wireless mobile devices for digital manufacture and provides a functional reference model based on this simplified unit cell of warp-knitted loops to simulate more realistic 3D warp knitted fabrics.