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1. Overview of the FEM classes The FEM represented by the class Domain is mainly composed by the modules represented by the abstract classes Node, Element, Material, Interface and ioDomain as shown in Fig. 2. The class Node contains nodal data, such as node number or nodal coordinates. Two instances of the NodalField class containing all nodal quantities at each node are linked to each node of the structure. The first one is relative to time t, the second one to t þ Dt: At the end of the increment, we just have to swap the references to those objects to transfer all quantities from one step to another (see step 2 of the explicit time integration flowchart in Box 1).

4] Langer SH, comparison A. A comparison of the floating-point performance of current computers. Comput Phys 1998;12(4):338– 45. [5] Cross JT, Masters I, Lewis RW. Why you should consider objectoriented programming techniques for finite element methods. Int J Numer Meth Heat Fluid Flow 1999;9:333 –47. [6] Hughes TJR. The Finite element method; linear static and dynamic finite element analysis. New York: Prentice-Hall; 1987. [7] Simo JC, Hughes TJR. Computational inelasticity. Berlin: Springer; 1998.

Initial conditions and initialization: n ¼ 0; s0 ¼ sðt0 Þ; x0 ¼ xðt0 Þ; v0 ¼ vðt0 Þ 2. Update quantities: n U n þ 1; sn ¼ sn21 ; xn ¼ xn21 ; vnþ1=2 ¼ vn21=2 3. Compute the time-step and update current time: tn ¼ tn21 þ Dt 4. Update nodal displacements: xn ¼ xn21 þ Dtvn21=2 ext 5. Compute internal and external force vector f int n ; fn 6. Integrate the conservative equations and compute accelerations: v_ n ¼ int M21 ðf ext n 2 fn Þ 7. Update nodal velocities: vnþ1=2 ¼ vn21=2 þ Dt_vn 8. Enforce essential boundary conditions: if node I on Gv 9.

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