Displacement Determination of a Uniformly Loaded Concrete Beam using Finite Element Analysis

— We analyzed the displacement state of a concrete beam subjected to a uniform load. The Mass (m), according to quantum theory is energy (E). This energy is in a constant state of flux. The continuous changes brought about by the displacement of particles in a solid, seems to deter normal explanation until a visible deformation occurs. Deformation usually occurs if displacement at the atomic and sub-atomic level are inhomogeneous. That is, there is variance in the path-lines of displacement. This differences in the path-line travelled by the particles between two points within a solid creates an extrema condition. Hence, the particles displaced can either take a straight path denoted ????(????), or a family of trajectories̅????(????). The variation between these two paths of displacements ????(????) ???????????? ????̅(????) , within a solid, is what determines the equilibrium configuration of a solid. If the variance is maximum, the solid will deform. If minimum or equal, the solid will then be stationary. This displacement analysis lays the mathematical foundation for the derivation of Euler-Lagrange equation of solid mechanics; with which, we derived the equivalent form of the governing differential equation from any given functional (F). Whose solution (displacement) ????(????) is obtained using finite element method