In this chapter, we discuss the finite element analysis procedure for two types of time-dependent problems: transient heat transfer and structural dynamics (or elastodynamics) problems. In the transient finite element analysis, similar to the discretization of the spatial domain, the continuous time axis is discretized into time steps for time-dependent solutions. Time integration schemes are used to calculate the solution at a given time step by using information already known from previous time steps. The time integration represents the major difference in the solution steps of FEA for time-dependent problems. This chapter contains two sections. The first section introduces the FEA procedure for transient heat transfer analysis by using a 2-D example problem. The second section discusses elastodynamic analysis by demonstrating the procedure of calculating the dynamic response of a 2-D cantilever beam, as well as finding its natural frequencies and vibrational modes. MATLAB codes for solving these problems are presented.
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