The Approximate Solution of the Nonlinear Exact Equation of Deflection of an Elastic Beam with the Galerkin Method

Calculating the large deflection of a cantilever beam is one common problems in engineering. The differential equation under deformation, or typical elastica problem, hard to approximate and solve with known solutions techniques Cartesian coordinates. exact elliptic functions are available, but not explicit expressions elementary expectation. This paper attempts nonlinear an elastic Galerkin method by successfully solving series algebraic equations as novel approach. solution based on trigonometric function assumed, coefficients fitted Chebyshev polynomials. numerical results show that third-order highly consistent function. effectiveness advantages further demonstrated.