Modified one-element method for exact dynamic responses of a beam by using the frequency domain spectral element method

다국어 초록 (Multilingual Abstract)

<P><B>Abstract</B></P> <P>In the spectral element method (SEM), there are two ways to deal with external loads applied to a structure member. One way is to represent the structure member as a single finite element subjected to effective nodal forces and moments at two end-nodes of the finite element, which is called the “one-element method” (OEM). The other way is to represent the structure member as two finite elements, with consideration of the external loads as nodal forces and moments applied at the joint node (i.e., the excitation point), which is called the “two-element method” (TEM). The OEM does not require the assembly of finite elements, but in general provides poor dynamic responses. On the other hand, the TEM requires the assembly of finite elements, but always provides exact dynamic responses. Based on this intrinsic exactness of the TEM, a new SEM-based solution technique called the “modified one-element method” (MOEM) is proposed. The MOEM is developed by analytically transforming the SEM-based two-element model into the form of the SEM-based one-element model and it can provide exact dynamic responses without the assembly of finite elements. Through numerical simulations, the accuracy of the OEM, TEM, and MOEM is evaluated.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Presented a new solution method for exact solutions by the spectral element method. </LI> <LI> Developed a modified one-element method (MOEM) as the new solution method. </LI> <LI> The exact MOEM results are obtained by adding correction terms to the OEM results. </LI> <LI> Verified the exactness of the proposed MOEM via numerical examples. </LI> </UL> </P>