# Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models
## 1 Introduction
The practical application was illustrated through an example, in which an FE model of a cylindrical rubber vibration isolator was updated using in-situ experimental data and sub-structure invariants without it being removed from an assembly. Since most of FE model updating techniques do not employ damping, [PERSON] et al. [17] proposed a two-step procedure that is able to update mass and stiffness matrices and, subsequently, identify the damping matrix. It allows accurate prediction of complex frequency response functions. The effectiveness of the proposed procedure was demonstrated by numerical examples as well as by actual experimental data. [PERSON] et al. [18] presented the use of FE model updating in civil structural applications. They proposed the method tailored to the needs of structural FE analysis of large size models. Its basis is an efficient model reduction strategy derived by slightly modifying the Lanczos projection, which in combination with a trust-region method allows matching the measured frequencies with the ones predicted by the parametric model. The authors performed several numerical experiments aimed to determine the optimal values of [PERSON]'s modulus and the mass density of building materials. The FE model updating can also be applied on composite materials. [PERSON] et al. provided a detailed overview of this topic [19]. In the case of composite structures, the response is highly dependent on the orientation of the fibers and the material properties of all constituents. [PERSON] et al. [20] developed an inverse method that minimizes the residual between the experimental and numerical results by adapting the stiffness properties in the FE calculation. The method is based on static tests and allows correct modelling of the fiber orientations and material properties. It was used to improve the structural response of two small scale marine composite propeller. The accuracy of the results was verified by comparing the natural frequencies. [PERSON] et al. [21] proposed a multi-level optimization approach for updating finite element models, in which the mass and stiffness related parameters are updated, respectively, in two different levels. The approach was employed for updating the finite element models of a composite flying-wing aircraft by using experimental results for both the aircraft and its components. The optimization results showed that the component responses may not match the test data when only using the test data for the complete model. When integrating the components' test data in the FE model updating, the responses for both the complete model and the components match the test data well. In their study [22], [PERSON] et al. focused on the assessment of a set of reliable composite material constitutive parameters, which are extracted using digital image correlation (DIC) and FE model updating. The uncertainty was induced by the measurement system noise in the DIC technique and the approximation error in the displacements and strains smoothing algorithm. Another problem where the FE model updating can be applied is the homogenization. Homogenization techniques allow to investigate the macroscopic behavior of a heterogeneous, porous or composite material, considering that the original material is replaced by an equivalent homogeneous material with comparable properties. [PERSON] et al. [23] presented a simple approach to study a hollow cylinder composite beam as it behaves like an isotropic one. The stiffness matrix of the equivalent 3D Euler-Bernoulli beam model was obtained using the proposed analytical method. Using this approach, the authors investigated the behavior of beams with different laminate configurations. [PERSON] et al. [24] performed the dynamic FE analysis of steel-polymer concrete beams, in which the highly heterogeneous polymer concrete was modelled as a linear isotropic material. Three models of beams differing in cross-sectional dimensions showed high agreement with experimentally obtained mode shapes and frequency response functions.