Dynamic high order numerical manifold method based on weighted residual method

SUMMARYHigh Order Numerical Manifold Method (HONMM) is a powerful method to solve static problems. A development of HONMM to achieve a dynamic solution with high accuracy and less computational cost is addressed in the current paper. In the developed method, the global approximation is obtained through increasing the order of local approximation functions without any Linear Dependence (LD) of the unknowns. The weighted residual formulations are modified to be used in dynamic high order simulation. Moreover, a modified Newmark method formulation is adjusted for time integration of high order equations. The superiority of the proposed method over the conventional NMM is demonstrated through a special beam example. The dynamic free fall block example is used to exhibit the removal of mass matrix singularity. As cases of dynamic analysis, beam free and forced vibrations are illustrated which include a moving load. Finally, a non‐uniform cross‐section beam under dynamic variable loads with accelerated motion is solved while demonstrating the capability of the new method such as simplicity, accuracy and time efficiency for simulation of complex dynamic problems. Copyright © 2014 John Wiley & Sons, Ltd.