**4. Summary**

In this chapter, first Authors elaborated the finite element method based mathematical formulation considering first-order shear deformation theory. Also explained the stiffness matric and compliance matrix and relationship between three dimensional stresses and strains. Authors also explained the state of in-plane stresses and inplane stains with mathematical formulation of isotropic and anisotropic materials. Here, authors also elaborated the transformation of stiffness matrixes and explained how scaler components are independent on coordinate system and vector as well as tensors are independent, but components of vectors and tensors are dependent on coordinate system.

The static and dynamic analysis of high rise building subjected to uniform pressure (*q*) and wind load (considered as triangular load as *W* = *q y*/*L*) and combination of both (*q/2* + (*q/2) y*/*L*) has been performed eight node shell 281 element through commercial finite element-based software ANSYS.

*Perspective Chapter: Dynamic Analysis of High-Rise Buildings Using Simplified Numerical… DOI: http://dx.doi.org/10.5772/intechopen.108556*

#### **Figure 13.**

*Fast Fourier Transform and phase portrait for first thre`e bending modes of cantilever plate.*

The large amplitude flexural vibration responses of isotropic and RCC flat panels is also investigated considering first 9 modes. It is found that 1st Torsion mode gives the softening responses whereas remaining bending, out-off plane bending and higher order torsion mode fives hardening effect.

Fast Fourier transform shows the amplitude verses time response and phase portrait gives displacement verses velocity response, represents effect mode shapes to design safe structures.
