On the objective stress rate in co-moving coordinate system

1989 ◽  
Vol 10 (2) ◽  
pp. 103-112 ◽  
Author(s):  
Shang Yong ◽  
Chen Zhi-da
Keyword(s):  
Coordinate System ◽  
Stress Rate ◽  
Moving Coordinate ◽  
Objective Stress Rate ◽  
Objective Stress

Elastic Soft-Core Sandwich Plates: Critical Loads and Energy Errors in Commercial Codes Due to Choice of Objective Stress Rate

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Jan Vorel ◽  
Zdeněk P. Bažant ◽  
Mahendra Gattu
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Finite Strain ◽  
Strain Tensor ◽  
Stress Rate ◽  
Soft Core ◽  
Sandwich Plates ◽  
The Core ◽  
Objective Stress Rate ◽  
Objective Stress

Most commercial finite element codes, such as ABAQUS, LS-DYNA, ANSYS and NASTRAN, use as the objective stress rate the Jaumann rate of Cauchy (or true) stress, which has two flaws: It does not conserve energy since it is not work-conjugate to any finite strain tensor and, as previously shown for the case of sandwich columns, does not give a correct expression for the work of in-plane forces during buckling. This causes no appreciable errors when the skins and the core are subdivided by several layers of finite elements. However, in spite of a linear elastic behavior of the core and skins, the errors are found to be large when either the sandwich plate theory with the normals of the core remaining straight or the classical equivalent homogenization as an orthotropic plate with the normals remaining straight is used. Numerical analysis of a plate intended for the cladding of the hull of a light long ship shows errors up to 40%. It is shown that a previously derived stress-dependent transformation of the tangential moduli eliminates the energy error caused by Jaumann rate of Cauchy stress and yields the correct critical buckling load. This load corresponds to the Truesdell objective stress rate, which is work-conjugate to the Green–Lagrangian finite strain tensor. The commercial codes should switch to this rate. The classical differential equations for buckling of elastic soft-core sandwich plates with a constant shear modulus of the core are shown to have a form that corresponds to the Truesdell rate and Green–Lagrangian tensor. The critical in-plane load is solved analytically from these differential equations with typical boundary conditions, and is found to agree perfectly with the finite element solution based on the Truesdell rate. Comparisons of the errors of various approaches are tabulated.

scholarly journals A Note on the Barotropic Forecast Using a Moving Coordinate System

1956 ◽  
Vol 34 (3) ◽  
pp. 164-168 ◽  
Author(s):  
S. Syono ◽  
K. Gambo ◽  
K. Miyakoda ◽  
M. Aihara ◽  
S. Manabe
Keyword(s):  
Coordinate System ◽  
Moving Coordinate

scholarly journals Operating on Tensors within Dynamic Coordinate Frames

2018 ◽  
Author(s):  
Keith C. Afas
Keyword(s):  
Coordinate System ◽  
Continuum Mechanics ◽  
Theoretical Models ◽  
Tensor Calculus ◽  
Dynamic Distortion ◽  
Coordinate Frames ◽  
Moving Coordinate ◽  
Calculus Of Moving Surfaces

This paper puts forward an alteration for Tensor Calculus utliized in a coordinate system which is under a dynamic distortion drawing inspiration from similar fields such as the Calculus of Moving Surfaces (CMS). The paper establishes transformation laws for Tensors within these regions and establishes Operators such as the Tensorial Field Derivative which enforce a Tensorial Transformation on Tensors defined within a Dynamically Moving coordinate system. This variation of Tensor Calculus can be utilized to observe how disciplines such as QFT and Continuum Mechanics would change to accomodate for a distorting coordinate system and can be utliized to develop new theoretical models which account for this temporal distortion particularly within Biological Settings.

The Motion Planning for Spherical Robot with Two Motors

2015 ◽  
Vol 789-790 ◽  
pp. 688-692
Author(s):  
Xin Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Angular Velocity ◽  
Motion Planning ◽  
Coordinate System ◽  
Optimization Problem ◽  
Kinematic Model ◽  
Pso Algorithm ◽  
Spherical Robot ◽  
Swarm Optimization ◽  
Moving Coordinate

In this paper, we proposed a spherical robot with two motors in the horizontal and vertical directions which derive the robot to do omni-directionally roll. Based on the structure of the robot, we derived the kinematic model using inertial and moving coordinate system. In order to minimize the energy of the system, an optimization problem with two optimization variables which are the parameters to control the angular velocity of the motors is given. After that, a particle swarm optimization (PSO) algorithm is used to solve the optimization problem. The simulation shows that the motion planning with the algorithm has high precision.

Oil Shale Retorting in a Bottom-Burning Retort

1981 ◽  
Vol 103 (2) ◽  
pp. 119-127
Author(s):  
K. S. Udell ◽  
H. R. Jacobs
Keyword(s):  
Experimental Study ◽  
Coordinate System ◽  
Combustion Front ◽  
Oil Shale ◽  
Thermal Processes ◽  
High Quality ◽  
Uniform Velocity ◽  
Moving Coordinate

An experimental study of a bottom-burning oil shale retort is described. It is shown that for a constant oxidizer flow the combustion front moves at a uniform velocity through the bed. This leads to the use of a moving coordinate system attached to the combustion front in evaluating the various thermal processes occurring in the retort. It is shown that the high quality of oil produced can be tied to a thermal refluxing not present in other retort processes.

On the Workspace of Closed-Loop Manipulators With Ground-Mounted Rotary-Linear Actuators and Finite Size Platform

1987 ◽  
Author(s):  
Tzu-Chen Weng ◽  
G. N. Sandor ◽  
Yongxian Xu ◽  
D. Kohli
Keyword(s):  
Coordinate System ◽  
Closed Loop ◽  
Finite Size ◽  
Degree Of Freedom ◽  
Moving Coordinate ◽  
Linear Actuators ◽  
Six Degree Of Freedom

Abstract This paper deals with the workspace of a closed-loop manipulator having three rotary-linear (R-L) actuators on ground-mounted cylindric joints, plus three revolute and three spheric pairs [1]. The workspace is defined as the reachable region of the origin of the moving coordinate system embedded in the six-degree-of-freedom platform of the manipulator. The regions in the workspace where the platform can rotate in any direction, cannot rotate or can rotate in only some directions have been defined as complete rotatability workspace (CRW), nonrotatability workspace (NRW) and partial rotatability workspace (PRW). Equations of the workspace of the platform which has a) complete theoretical rotatability and b) nonrotatability (when its center is on the boundary of the workspace) are respectively derived. The reachable region of the center of the platform, where this center remains in a plane with a given platform orientation, is also studied.

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