Large Deflections of Beam Subject to Three-points Bending
Provides a more accurate analytical solution for beam deflection problems in structural mechanics, but the approach is incremental and domain-specific.
The paper derives an exact solution for large deflections of an elastic beam under three-point bending using Jacobi elliptic functions, and provides an approximate polynomial formula for load versus deflection. Numerical results are compared with existing literature.
In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several examples that illustrate a use of the solution are discussed. The obtained numerical results are compared with results of other authors. Approximation formula by which the beam load is given as polynomial function of beam deflection is also derived. The range of applicability of the approximation is illustrated by numerical example.