Large Deformation Analysis and Synthesis of Elastic Closed-loop Mechanism Made of a Certain Spring Wire Described by Free Curves

Recently novel mechanisms with compact size and without many mechanical elements such as bearing are strongly required for medical devices such as surgical operation devices. This paper describes analysis and synthesis of elastic link mechanisms of a single spring beam which can be manufactured by NC coiling machines. These mechanisms are expected as disposable micro forceps. Smooth Curvature Model（SCM） with 3rd order Legendre polynomial curvature functions is applied to calculate large deformation of a curved cantilever beam by taking account of the balance between external and internal elastic forces and moments. SCM is then extended to analyze large deformation of a closed-loop curved elastic beam which is composed of multiple free curved beams. A closed-loop elastic link is divided into two free curved cantilever beams each of which is assumed as serially connected free curved cantilever beams described with SCM. The sets of coefficients of Legendre polynomials of SCM in all free curved cantilever beams are determined by taking account of the force and moment balance at connecting point where external input force is applied. The sets of coefficients of Legendre polynomials of a nonleaded closed-loop elastic link are optimized to design a link mechanism which can generate specified output motion due to input force applied at the assumed dividing point. For example, two planar micro grippers with a single pulling input force are analyzed and designed. The elastic deformation analyzed with proposed method agrees very well with that calculated with FEM. The designed micro gripper can generate the desired pinching motion. The proposed method can contribute to design compact and simple elastic mechanisms without high calculation costs.

A MIXED VARIATIONAL FORMULATION FOR LARGE DEFORMATION ANALYSIS OF PLATES

A mixed vuriational formulation for large deformation analysis of plates is introduced. In this formulation the equilibrium ami compatibility equations are satisfied identically by means of stress functions and displacement components, respectively, and the constitu,lye equations are satisfied in a least square sense. An example is solved and the results are compared with those available in the literature.Further, the functional is particularized for buckling analysis of plates and a simple example is solved to illustrate the theory.

Large deformation simulations of geomaterials using moving particle semi-implicit method

Numerical simulation tools are required to describe large deformations of geomaterials for evaluating the risk of geo-disasters. This study focused on moving particle semi-implicit(MPS) method, which is a Lagrangian gridless particle method, and investigated its performance and stability to simulate large deformation of geomaterials. A calculation method was developed using geomaterials modeled as Bingham fluids to improve the original MPS method and enhance its stability. Two numerical tests showed that results from the improved MPS method was in good agreement with the theoretical value.Furthermore, numerical simulations were calibrated by laboratory experiments. It showed that the simulation results matched well with the experimentally observed free-surface configurations for flowing sand. In addition, the model could generally predict the time-history of the impact force. The MPS method could be a useful tool to evaluate large deformation of geomaterials.

Large Deformation Beam/Cable Element with Implicit Kinematic Model

This paper proposes a 3D 2-node element for beams and cables. Main improvements of the element are two new interpolation functions for beam axis and cross-sectional rotation. New interpolation functions employ implicit functions to simulate large deformations. In the translational interpolation function, two parameters which affect lateral deflection geometry are defined implicitly through nonlinear equations. The proposed translational interpolation function is shown to be more accurate than Hermitian function at large deformations. In the rotational interpolation function, twist rate is defined implicitly through a torsional continuity equation. Cross-sectional rotation which is strictly consistent to beam axis is obtained through separate bending rotation interpolation and torsional rotation interpolation. The element model fully accounts for geometric nonlinearities and coupling effects,and thus,can simulate cables with zero bending stiffness. Stiffness matrix and load vector have been derived using symbolic computation. Source code has been generated automatically.Numerical examples show that the proposed element has significantly higher accuracy than conventional 2-node beam elements under the same meshes for geometrically nonlinear problems.

Failure of levees induced by toe uplift:Investigation of post-failure behavior using material point method

Levees are essential structures in flood defense systems,and their failures can lead to devastating consequences on the surrounding territories.One of the failure mechanisms mostly controlled by the foundation soil stratigraphy is the instability of the land side slope,triggered by the development of high uplift pressures in the foundation.This complex phenomenon has been investigated experimentally with centrifuge tests or large-scale tests and numerically with the limit equilibrium method(LEM)and the finite element method(FEM).In this work,we applied a multiphase formulation of the material point method(MPM)to analyze the development of toe uplift instability mechanism,from the onset of failure to large displacements.The numerical model is inspired by an experiment carried out in a geotechnical centrifuge test by Allersma and Rohe(2003).The comparison with the experiment allows for understanding critical pore pressure triggering large displacements in the foundation soils.Moreover,we numerically evaluated the impact of different values of foundation soils’hydraulic conductivity on the failure mechanism.The results show that hydraulic conductivity mainly influences the time of failure onset and the extension of shear localization at depth.Finally,the advantages of using large displacement approaches in the safety assessment of earth structures are discussed.Unlike FEM,there are no issues with element distortions generating difficulties with numerical convergence,allowing for full postfailure reproduction.This capability permits precise quantification of earth structure damages and post-failure displacements.The ensuing reinforcement systems’design is no longer over-conservative,with a significant reduction in associated costs.

A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth,Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.