Mixed Natural Neighbor Galerkin Method for 3D Couple-Stress Elasticity

2010 ◽  
Vol 37-38 ◽  
pp. 667-670
Author(s):  
Kai Wang ◽  
Shen Jie Zhou ◽  
Zhi Feng Nie
Keyword(s):  
Galerkin Method ◽  
Size Effects ◽  
Couple Stress ◽  
Degrees Of Freedom ◽  
Characteristic Length ◽  
Three Dimensional ◽  
Discrete Equations ◽  
Natural Neighbor ◽  
Couple Stress Elasticity ◽  
Geometrical Constraints

Based on the constrained variational principle, the mixed multi-variable natural neighbor Galerkin method for couple-stress elasticity is proposed for three-dimensional problems. The displacements and micro-rotations are taken to be independent nodal degrees of freedom, and the geometrical constraints between them are enforced through Lagrange multipliers. The C0-continuous non-Sibsonain interpolation is used to obtain the discrete equations. The proposed method is tested by the numerical example and the results show that strong size effects are observed when the length of deformation field and the characteristic length of the material are comparable.

Size effects in two-dimensional layered materials modeled by couple stress elasticity

2021 ◽  
Author(s):  
Wipavee Wongviboonsin ◽  
Panos A. Gourgiotis ◽  
Chung Nguyen Van ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Size Effects ◽  
Couple Stress ◽  
Layered Materials ◽  
Two Dimensional ◽  
Couple Stress Elasticity

C1 Natural Element Method for Couple-Stress Elasticity

2011 ◽  
Vol 105-107 ◽  
pp. 370-373
Author(s):  
Ru Jun Han ◽  
Zhi Feng Nie
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Couple Stress ◽  
Shape Functions ◽  
Galerkin Scheme ◽  
Natural Neighbor ◽  
Natural Element Method ◽  
Couple Stress Elasticity ◽  
Natural Element ◽  
Element Method

The shape functions in C1 natural element method (C1 NEM) are built upon the natural neighbor interpolation (NNI), and realize the interpolation to nodal function and nodal gradient values, so that the essential boundary conditions (EBCs) can be imposed directly in a Galerkin scheme for the partial differential equations (PDEs). In the present paper, C1 NEM for couple-stress (CS) elasticity is constructed, and the typical example which has analytical solutions is presented to illustrate the effectiveness of the constructed method.

An Embedded Elliptic Nano-Fiber in Anti-Plane Strain Couple Stress Elasticity

2008 ◽  
Author(s):  
Hossein M. Shodja ◽  
Hamed Haftbaradaran
Keyword(s):  
Size Effect ◽  
Isotropic Material ◽  
Couple Stress ◽  
Characteristic Length ◽  
Couple Stress Theory ◽  
Infinite Medium ◽  
Stress Theory ◽  
Couple Stress Elasticity ◽  
Nano Fiber ◽  
Continuum Theories

The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem.

Three-dimensional contact analysis with couple stress elasticity

2019 ◽  
Vol 153-154 ◽  
pp. 369-379 ◽  
Author(s):  
Yuxing Wang ◽  
Xin Zhang ◽  
Huoming Shen ◽  
Juan Liu ◽  
Bo Zhang ◽  
...  
Keyword(s):  
Couple Stress ◽  
Three Dimensional ◽  
Contact Analysis ◽  
Couple Stress Elasticity

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

scholarly journals Asymmetry in Three-Dimensional Sprinting with and without Running-Specific Prostheses

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 580
Author(s):  
Anna Lena Emonds ◽  
Katja Mombaur
Keyword(s):  
Degrees Of Freedom ◽  
Body Position ◽  
Three Dimensional ◽  
Problem Formulation ◽  
Contact Phase ◽  
Individual Level ◽  
Lower Trunk ◽  
Floating Base ◽  
The Asymmetry ◽  
Limb Asymmetry

As a whole, human sprinting seems to be a completely periodic and symmetrical motion. This view is changed when a person runs with a running-specific prosthesis after a unilateral amputation. The aim of our study is to investigate differences and similarities between unilateral below-knee amputee and non-amputee sprinters—especially with regard to whether asymmetry is a distracting factor for sprint performance. We established three-dimensional rigid multibody models of one unilateral transtibial amputee athlete and for reference purposes of three non-amputee athletes. They consist of 16 bodies (head, ipper, middle and lower trunk, upper and lower arms, hands, thighs, shanks and feet/running specific prosthesis) with 30 or 31 degrees of freedom (DOFs) for the amputee and the non-amputee athletes, respectively. Six DOFs are associated with the floating base, the remaining ones are rotational DOFs. The internal joints are equipped with torque actuators except for the prosthetic ankle joint. To model the spring-like properties of the prosthesis, the actuator is replaced by a linear spring-damper system. We consider a pair of steps which is modeled as a multiphase problem with each step consisting of a flight, touchdown and single-leg contact phase. Each phase is described by its own set of differential equations. By combining motion capture recordings with a least squares optimal control problem formulation including constraints, we reconstructed the dynamics of one sprinting trial for each athlete. The results show that even the non-amputee athletes showed less symmetrical sprinting than expected when examined on an individual level. Nevertheless, the asymmetry is much more pronounced in the amputee athlete. The amputee athlete applies larger torques in the arm and trunk joints to compensate the asymmetry and experiences a destabilizing influence of the trunk movement. Hence, the inter-limb asymmetry of the amputee has a significant effect on the control of the sprint movement and the maintenance of an upright body position.

Three-dimensional asymmetric maximum weight lifting prediction considering dynamic joint strength

2021 ◽  
pp. 095441192098703
Author(s):  
Rahid Zaman ◽  
Yujiang Xiang ◽  
Jazmin Cruz ◽  
James Yang
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Three Dimensional ◽  
Optimization Method ◽  
Weight Lifting ◽  
Joint Torque ◽  
Maximum Weight ◽  
Angular Velocities ◽  
Asymmetric Lifting

In this study, the three-dimensional (3D) asymmetric maximum weight lifting is predicted using an inverse-dynamics-based optimization method considering dynamic joint torque limits. The dynamic joint torque limits are functions of joint angles and angular velocities, and imposed on the hip, knee, ankle, wrist, elbow, shoulder, and lumbar spine joints. The 3D model has 40 degrees of freedom (DOFs) including 34 physical revolute joints and 6 global joints. A multi-objective optimization (MOO) problem is solved by simultaneously maximizing box weight and minimizing the sum of joint torque squares. A total of 12 male subjects were recruited to conduct maximum weight box lifting using squat-lifting strategy. Finally, the predicted lifting motion, ground reaction forces, and maximum lifting weight are validated with the experimental data. The prediction results agree well with the experimental data and the model’s predictive capability is demonstrated. This is the first study that uses MOO to predict maximum lifting weight and 3D asymmetric lifting motion while considering dynamic joint torque limits. The proposed method has the potential to prevent individuals’ risk of injury for lifting.

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