Data for publication: "Overcoming stretching and shortening assumptions in Euler-Bernoulli theory using nonlinear Hencky’s beam models: applicable to partly-shortened and partly-stretched beams"

The dataset accompanying the publication "Overcoming stretching and shortening assumptions in Euler-Bernoulli theory using nonlinear Hencky's beam models: applicable to partly-shortened and partly-stretched beams" comprises the following files:JSV_tex-file-and-figures.zip:This ZIP archive contains the LaTeX source files and associated figures used in the preparation of the manuscript. The LaTeX files are in plain text format, compatible with any text editor, and can be compiled using open-source LaTeX distributions such as TeX Live or MiKTeX. The figures are provided in standard formats (JPEG) that are widely supported by various image viewers and editing software.NH_BeamModel.m:This MATLAB script is part of the supplementary materials accompanying the paper and demonstrates the mathematical models and computations used for the nonlinear Hencky's beam model (NH). The code generates the final figure in our article (Fig. 16) and allows readers to recreate additional plots from the study by adjusting input parameters. We hope these resources enhance understanding of NH and support future research in obtaining beam configuration results. MATLAB is a proprietary software.GalerkinVsHencky.zip:This ZIP archive (195.1 KB) contains code files comparing the Galerkin method with Hencky's beam model results. The files are in MATLAB (.m), Maple (.mpl), and Mathematica (.nb) formats. This ZIP archive can be extracted using standard tools available on most operating systems.Research Project OverviewThis research addresses limitations in the traditional Euler-Bernoulli beam theory, particularly its assumptions about stretching and shortening in beams. In certain boundary conditions, such as a cantilever with a horizontal spring at its tip, beams may experience partial shortening or stretching based on the spring stiffness. The Euler-Bernoulli model often fails to capture the geometric nonlinearity under these conditions, so nonlinear Hencky’s beam models are introduced to better represent these behaviors.The study validates Hencky’s models against the nonlinear Euler-Bernoulli model using the Galerkin method, with examples like cantilever and clamped-clamped beams representing shortened and stretched configurations. For a cantilever with variable horizontal stiffness, the nonlinear Hencky model reveals that increasing horizontal stiffness transitions the system from softening to linear and then to hardening as it approaches the second resonance frequency, indicating a potential bifurcation point.While nonlinear Hencky’s models are computationally intensive, they offer a robust alternative to overcome the simplifications in Euler-Bernoulli theory. These models enable an in-depth nonlinear analysis of beams that experience partial stretching or shortening, thus enhancing structural analysis and design.