An ultra-accurate isogeometric dynamic analysis is presented.The key ingredient of the proposed methodology is the development of isogeometric higher order mass matrix.A new one-step method is proposed for the construction of higher order mass matrix.In this approach,an adjustable mass matrix is formulated through introducing a set of mass parameters into the consistent mass matrix under the element mass conservation condition.Then the semi-discrete frequency derived from the free vibration equation with the adjustable mass matrix is served as a measure to optimize the mass parameters.In 1D analysis,it turns out that the present one-step method can perfectly recover the existing reduced bandwidth mass matrix and the higher order mass matrix by choosing different mass parameters.However,the employment of the proposed one-step method to the2D membrane problem yields a remarkable gain of solution accuracy compared with the higher order mass matrix generated by the original two-step method.Subsequently a full-discrete isogeometric transient analysis algorithm is presented by using the Newmark time integration scheme and the higher order mass matrix.The full-discrete frequency is derived to assess the accuracy of space-time discretization.Finally a set of numerical examples are presented to evaluate the accuracy of the proposed method,which show that very favorable solution accuracy is achieved by the present dynamic isogeometric analysis with higher order mass formulation compared with that obtained from the standard consistent mass approach.
