Cartesian and piecewise parametric large deflection solutions of tip point loaded Euler–Bernoulli cantilever beams

• Studied large deflection solution of Euler–Bernoulli cantilever beams subjected to combined tip point loading.
• Developed cartesian large deflection solutions for general tip point loading.
• Developed a new closed form solution for the case of a large pure end-force.
• Developed rapidly convergent piecewise parametric large deflection solutions for general tip point loading.
• Coded the solutions as BeamSol, a stand-alone user-friendly black-box large deflection beam solver.

This paper focuses on the large deflection solutions of Euler–Bernoulli cantilever beams loaded at the tip with a force and moment. Cartesian large deflection solutions are given for general tip point loading, as well as a new closed form solution for the case of a large end-force only. Additionally, we develop piecewise parametric large deflection solutions, which can efficiently and effectively quantify the inherently nonlinear and complex load, deformation, and energy relationships exhibited by compliant mechanisms, thus, paving the way for the emergence of novel compliant mechanism syntheses. The utilization of the proposed solution methodology can help the precision engineering community in the design of new devices with fixed size and no dependence on the load magnitudes. We coded the solutions as BeamSol, a stand-alone user-friendly black-box solver, which is envisioned to help researchers in engineering analyses and syntheses of beam applications.