Finite Element Modeling of Geometrically Exact Shell With Large Deformation and Rotation

This paper developed a new geometrically exact shell element to model the relatively thin structures with large deformations and arbitrary rigid motions. The deformations were well decoupled from rigid motions by using the direct modeling approach. The rotation-free Green-Lagrange strain tensor described the large deformations together with geometrical nonlinearities. Meanwhile, the Wiener-Milenković parameter was applied to vectorial parameterize the arbitrary rotations of the fiber avoiding the singularities usually occurred in the classical shell formula. This paper also designed a new interpolating algorithm without losing objectivity to discretize the vectorial parameters, which improves the robustness of new shell element. The application of Mixed Interpolation of Tensorial Components with 9 nodes (MITC9) makes the shell element shear-locking free and with second-order accuracy. Each node contains five degrees of freedom, three for translations and two for rotations, achieving a minimal set representation of arbitrary motions. These innovations contribute to a new shell formula featuring high computational efficiency with good accuracy. Finally, two flexible multibody dynamic models are discretized by this new shell element. The numerical simulation results of the new shell element have been verified to demonstrate the capability of new shell element dealing with large deformations and arbitrary motions of thin structures.

A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

In this paper, we derive the weak form for clamped plates composed of incompressible neo-Hookean material from the uniformly valid asymptotic plate theory. By using the finite-element software COMSOL, we study the numerical solutions of the weak form. We show the accuracy and the efficiency of the weak form by comparing the numerical results for the two-dimensional weak form and a three-dimensional model. As a basis for comparison we choose numerical values of the displacement, the second Piola–Kirchhoff stress, and the Green–Lagrange strain at the bottom. The numerical simulations are performed for three different cases of thickness–span ratios, including (1) very thin plate, (2) thin plate, and (3) moderately thick plate. The results show that the uniformly valid plate theory is a reliable and implementable plate theory for even moderately thick plates with large deformations.

Continuum modeling and vibration analysis of cable-harnessed plate structures of periodic patterns

Over the past decade, modeling of cable-harnessed space structures has received special attention due to the need for better accuracies than the existing models. As these structures become more lightweight upon the advancements in the materials science it is imperative to further consider accurate models in which the dynamic effects of the added cables are better accounted for. Researchers have heavily focused on creating models for cable-harnessed beam-like structures, while very few works have considered plate-like structures. The proposed research aims at the development of an analytical model for cable-harnessed plate-like structures. Cables are assumed to be periodic in geometry to allow for the application of an energy-equivalent homogenization technique. To begin with, a linear displacement field and a second-order Green-Lagrange strain tensor for strain-displacement relationships are considered. The strain and kinetic energies of the fundamental element are found using these relations. The repeated pattern of the fundamental element over the area of the plate structure allows for the employment of the homogenization approach in which the kinetic and strain energies per area of the fundamental element are found and assumed to remain the same as an equivalent homogenized solid plate-like element. The governing dynamic Partial Differential Equations (PDEs) are found using the Hamilton’s principle. The results are validated using finite element analysis. A detailed parametric analysis is also performed to investigate the effects of various cable parameters and wrapping patterns on the dynamics of the host structure.

Temperature-Dependent Vibration of Various Types of Sandwich Beams with Porous FGM Layers

By using a high order sandwich beams theory which is modified by considering the transverse flexibility of the core, free vibration characteristics of two models of sandwich beams are studied in this paper. In type-I, functionally graded layers coat a homogeneous core, and in type-II, an FG core is covered by homogeneous face sheets. To increase the accuracy of the model of the FGM properties, even and uneven porosity distributions are applied, and all materials are considered temperature-dependent. Nonlinear Lagrange strain and thermal stresses of the face sheets and in-plane strain of the core are considered. To obtain the governing equations of motion, Hamilton’s principle is used and a Galerkin method is used to solve them for simply supported and clamped boundary conditions. To verify the results of this study, they are compared with the results of literatures. Also, the effect of variation of temperature, some geometrical parameters and porosities on the frequency are studied.

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

Sustained scleral stiffening in rats after a single genipin treatment

Scleral stiffening has been proposed as a therapy for glaucoma and myopia. Previous in vivo studies have evaluated the efficacy of scleral stiffening after multiple treatments with a natural collagen crosslinker, genipin. However, multiple injections limit clinical translatability. Here, we examined whether scleral stiffening was maintained after four weeks following a single genipin treatment. Eyes from brown Norway rats were treated in vivo with a single 15 mM genipin retrobulbar injection, sham retrobulbar injection, or were left naive. Eyes were enucleated either 1 day or four weeks post-injection and underwent whole globe inflation testing. We assessed first principal Lagrange strain of the posterior sclera using digital image correlation as a proxy for scleral stiffness. Four weeks post-injection, genipin treatment resulted in a 58% reduction in scleral strain as compared to controls ( p = 0.005). We conclude that a single in vivo injection of genipin effectively stiffened rat sclera for at least four weeks which motivates further functional studies and possible clinical translation of genipin-induced scleral stiffening.

Analysis of the Elastoplastic Response in the Torsion Test Applied to a Cylindrical Sample

This work presents an experimental and numerical analysis of the mechanical behavior of a fixed-end SAE 1045 steel cylindrical specimen during the torsion test. To this end, an iterative numerical–experimental methodology is firstly proposed to assess the material response in the tensile test using a large strain elastoplasticity-based model solved in the context of the finite element method. Then, a 3D numerical simulation of the deformation process of the torsion test is tackled with this previously characterized model that proves to be able to predict the development of a high and localized triaxial stress and strain fields caused by the presence of high levels of angular deformation. Finally, the obtained numerical results are analytically studied with the cylindrical components of the Green–Lagrange strain tensor and experimentally validated with the measurements of shear strains via Digital Image Correlation (DIC) and the corresponding torque – twist angle curve.

Strain Mapping From Four-Dimensional Ultrasound Reveals Complex Remodeling in Dissecting Murine Abdominal Aortic Aneurysms

Current in vivo abdominal aortic aneurysm (AAA) imaging approaches tend to focus on maximum diameter but do not measure three-dimensional (3D) vascular deformation or strain. Complex vessel geometries, heterogeneous wall compositions, and surrounding structures can all influence aortic strain. Improved understanding of complex aortic kinematics has the potential to increase our ability to predict aneurysm expansion and eventual rupture. Here, we describe a method that combines four-dimensional (4D) ultrasound and direct deformation estimation to compute in vivo 3D Green-Lagrange strain in murine angiotensin II-induced suprarenal dissecting aortic aneurysms, a commonly used small animal model. We compared heterogeneous patterns of the maximum, first-component 3D Green-Lagrange strain with vessel composition from mice with varying AAA morphologies. Intramural thrombus and focal breakage in the medial elastin significantly reduced aortic strain. Interestingly, a dissection that was not detected with high-frequency ultrasound also experienced reduced strain, suggesting medial elastin breakage that was later confirmed via histology. These results suggest that in vivo measurements of 3D strain can provide improved insight into aneurysm disease progression. While further work is needed with both preclinical animal models and human imaging studies, this initial murine study indicates that vessel strain should be considered when developing an improved metric for predicting aneurysm growth and rupture.

Analytical Study of Coupling Effects for Vibrations of Cable-Harnessed Beam Structures

This paper presents a distributed parameter model to study the effects of the harnessing cables on the dynamics of a host structure motivated by space structures applications. The structure is modeled using both Euler–Bernoulli and Timoshenko beam theories (TBT). The presented model studies the effects of coupling between various coordinates of vibrations due to the addition of the cable. The effects of the cable's offset position, pretension, and radius are studied on the natural frequencies of the system. Strain and kinetic energy expressions using linear displacement field assumptions and Green–Lagrange strain tensor are developed. The governing coupled partial differential equations for the cable-harnessed beam that includes the effects of the cable pretension are found using Hamilton's principle. The natural frequencies from the coupled Euler, Bernoulli, Timoshenko and decoupled analytical models are found and compared to the results of the finite element analysis (FEA).