• Title/Summary/Keyword: Lagrange Equation

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Nonlinear numerical modelling for the effects of surface explosions on buried reinforced concrete structures

  • Nagy, N.;Mohamed, M.;Boot, J.C.
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.1-18
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    • 2010
  • The analysis of structure response and design of buried structures subjected to dynamic destructive loads have been receiving increasing interest due to recent severe damage caused by strong earthquakes and terrorist attacks. For a comprehensive design of buried structures subjected to blast loads to be conducted, the whole system behaviour including simulation of the explosion, propagation of shock waves through the soil medium, the interaction of the soil with the buried structure and the structure response needs to be simulated in a single model. Such a model will enable more realistic simulation of the fundamental physical behaviour. This paper presents a complete model simulating the whole system using the finite element package ABAQUS/Explicit. The Arbitrary Lagrange Euler Coupling formulation is used to model the explosive charge and the soil region near the explosion to eliminate the distortion of the mesh under high deformation, while the conventional finite element method is used to model the rest of the system. The elasto-plastic Drucker-Prager Cap model is used to model the soil behaviour. The explosion process is simulated using the Jones-Wilkens-Lee equation of state. The Concrete Damage Plasticity model is used to simulate the behaviour of concrete with the reinforcement considered as an elasto-plastic material. The contact interface between soil and structure is simulated using the general Mohr-Coulomb friction concept, which allows for sliding, separation and rebound between the buried structure surface and the surrounding soil. The behaviour of the whole system is evaluated using a numerical example which shows that the proposed model is capable of producing a realistic simulation of the physical system behaviour in a smooth numerical process.

Kinematic and Dynamic Analyses of Human Arm Motion

  • Kim, Junghee;Cho, Sungho;Lee, Choongho;Han, Jaewoong;Hwang, Heon
    • Journal of Biosystems Engineering
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    • v.38 no.2
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    • pp.138-148
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    • 2013
  • Purpose: Determining an appropriate path is a top priority in order for a robot to maneuver in a dynamically efficient way especially in a pick-and-place task. In a non-standardized work environment, current robot arm executes its motion based on the kinematic displacements of joint variables, though resulting motion is not dynamically optimal. In this research we suggest analyzing and applying motion patterns of the human arm as an alternative to perform near optimum motion trajectory for arbitrary pick-and-place tasks. Methods: Since the motion of a human arm is very complicated and diverse, it was simplified into two links: one from the shoulder to the elbow, and the other from the elbow to the hand. Motion patterns were then divided into horizontal and vertical components and further analyzed using kinematic and dynamic methods. The kinematic analysis was performed based on the D-H parameters and the dynamic analysis was carried out to calculate various parameters such as velocity, acceleration, torque, and energy using the Newton-Euler equation of motion and Lagrange's equation. In an attempt to assess the efficacy of the analyzed human motion pattern it was compared to the virtual motion pattern created by the joint interpolation method. Results: To demonstrate the efficacy of the human arm motion mechanical and dynamical analyses were performed, followed by the comparison with the virtual robot motion path that was created by the joint interpolation method. Consequently, the human arm was observed to be in motion while the elbow was bent. In return this contributed to the increase of the manipulability and decrease of gravity and torque being exerted on the elbow. In addition, the energy required for the motion decreased. Such phenomenon was more apparent under vertical motion than horizontal motion patterns, and in shorter paths than in longer ones. Thus, one can minimize the abrasion of joints by lowering the stress applied to the bones, muscles, and joints. From the perspectives of energy and durability, the robot arm will be able to utilize its motor most effectively by adopting the motion pattern of human arm. Conclusions: By applying the motion pattern of human arm to the robot arm motion, increase in efficiency and durability is expected, which will eventually produce robots capable of moving in an energy-efficient manner.

An efficient 2.5D inversion of loop-loop electromagnetic data (루프-루프 전자탐사자료의 효과적인 2.5차원 역산)

  • Song, Yoon-Ho;Kim, Jung-Ho
    • Geophysics and Geophysical Exploration
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    • v.11 no.1
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    • pp.68-77
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    • 2008
  • We have developed an inversion algorithm for loop-loop electromagnetic (EM) data, based on the localised non-linear or extended Born approximation to the solution of the 2.5D integral equation describing an EM scattering problem. Source and receiver configuration may be horizontal co-planar (HCP) or vertical co-planar (VCP). Both multi-frequency and multi-separation data can be incorporated. Our inversion code runs on a PC platform without heavy computational load. For the sake of stable and high-resolution performance of the inversion, we implemented an algorithm determining an optimum spatially varying Lagrangian multiplier as a function of sensitivity distribution, through parameter resolution matrix and Backus-Gilbert spread function analysis. Considering that the different source-receiver orientation characteristics cause inconsistent sensitivities to the resistivity structure in simultaneous inversion of HCP and VCP data, which affects the stability and resolution of the inversion result, we adapted a weighting scheme based on the variances of misfits between the measured and calculated datasets. The accuracy of the modelling code that we have developed has been proven over the frequency, conductivity, and geometric ranges typically used in a loop-loop EM system through comparison with 2.5D finite-element modelling results. We first applied the inversion to synthetic data, from a model with resistive as well as conductive inhomogeneities embedded in a homogeneous half-space, to validate its performance. Applying the inversion to field data and comparing the result with that of dc resistivity data, we conclude that the newly developed algorithm provides a reasonable image of the subsurface.