Abstract
A family of explicit methods is proposed. Numerical properties of this family for linear elastic systems are exactly the same as those of the Newmark family method since they have the same characteristic equation. A subfamily of this family possesses unconditional stability for linear elastic systems. However, the most important aspects of this subfamily are the possibility of unconditional stability for nonlinear systems and second-order accuracy. The possibility of unconditional stability and second-order accuracy allows using a large time step; and the explicitness of each time step involves no iterative procedure. Hence, many computational efforts can be saved.
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