This paper addresses the development of the modified adaptive dynamic relaxation (maDR) method. Through a critical review of the merits and disadvantages of previous studies, the primary physical approaches for improving the efficiency of the method are discussed. Emphases are placed on the selection of initial vectors and the calculation of fictitious damping factors. A variety of engineering problems, linear and non-linear as well as isotropic and anisotropic problems, are chosen to demonstrate the applicability and efficiency of the modified method. It is concluded that selection of initial vectors is only suitable for one type of engineering problems. However, a proper evaluation of fictitious damping and its combination with initial vector selection form a more general way to improve the efficiency of the maDR method.

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