David C. Kellermann

In-Plane Nonlinear Buckling of Funicular Arches

This paper presents a numerical technique to determine the full pre-buckling and post-buckling equilibrium path for elastic funicular arches. The formulation includes the effects of shear deformations and geometric nonlinearity due to large deformations. The Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are considered without approximation. The finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for the internal actions are based on a hyperelastic constitutive model. Using the differential equilibrium equations and the constitutive laws, the nonlinear buckling behavior of some typical funicular arches are investigated using the trapezoid method with Richardson extrapolation enhancement. The results are validated by using the finite element package ANSYS and solutions available in the literature. Examples include parabolic arches under a uniformly distributed gravity load, a catenary under a distributed load along the arch and a catenary arch under an overburden load. Parametric studies are performed to identify the factors that influence the nonlinear buckling of funicular arches. The axial to shear rigidity ratio is shown to have a significant effect on the buckling load and the buckling mode shape.

Intrinsic Decomposition of The Stretch Tensor for Fibrous Media

This paper presents a novel mechanism for the description of fibre reorientation based on the decomposition of the stretch tensor according to a given material’s intrinsic constitutive properties. This approach avoids the necessity for fibre directors, structural tensors or specialised model such as the ideal fibre reinforced model, which are commonly applied to the analysis of fibre kinematics in the finite deformation of fibrous media for biomechanical problems. The proposed approach uses Intrinsic‐Field Tensors (IFTs) that build upon the linear orthotropic theory presented in a previous paper entitled Strongly orthotropic continuum mechanics and finite element treatment. The intrinsic decomposition of the stretch tensor therein provides superior capacity to represent the intermediary kinematics driven by finite orthotropic ratios, where the benefits are predominantly expressed in cases of large deformation as is typical in the biomechanical studies. Satisfaction of requirements such as Material Frame‐I...