A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy

2000 ◽  
Vol 68 (1) ◽  
pp. 109-114 ◽  
Author(s):  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Spherical Shell ◽  
Stress Analysis ◽  
Matrix Theory ◽  
Three Dimensional ◽  
The State ◽  
State Variables ◽  
State Equations ◽  
Independent State ◽  
Spherical Isotropy ◽  
Constant Coefficients

This paper presents an exact static stress analysis of a multilayered elastic spherical shell (hollow sphere) completely based on three-dimensional elasticity for spherical isotropy. Two independent state equations are derived after introducing three displacement functions and two stress functions. In particular, a variable substitution technique is used to derive the state equations with constant coefficients. Matrix theory is then employed to obtain the relationships between the state variables at the upper and lower surfaces of each lamina. By virtue of the continuity conditions between two adjacent layers, a second-order linear algebraic equation and a fourth-order one about the boundary variables at the inner and outer surfaces of a multilayered spherical shell are obtained. Numerical examples are presented to show the effectiveness of the present method.

The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

1971 ◽  
Vol 93 (4) ◽  
pp. 1261-1267 ◽  
Author(s):  
D. L. Bartel ◽  
E. J. Haug ◽  
Kwan Rim
Keyword(s):  
Nonlinear Programming ◽  
Mechanical Design ◽  
The State ◽  
Steepest Descent ◽  
Mathematical Programming Problem ◽  
State Variables ◽  
State Equations ◽  
Design Problems ◽  
Out Of Plane ◽  
Plane Frames

This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

Static Analysis of Thick Laminated Beams: Two-Dimensional Elasticity Solutions via Differential Quadrature

2005 ◽  
Vol 475-479 ◽  
pp. 1067-1072
Author(s):  
Chaofeng Lü ◽  
Ying Gao ◽  
W.Q. Chen
Keyword(s):  
Present Method ◽  
Matrix Theory ◽  
Laminated Composite ◽  
Static Problem ◽  
State Equation ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
State Variables ◽  
State Equations ◽  
Elasticity Solutions

This paper intends to present two-dimensional elasticity solutions for static problem of thick laminated composite beams using a hybrid method of state-space-based differential quadrature. The technique of differential quadrature is employed to reduce the partial differential state equations into the ordinary differential ones at all arbitrary sampling points for each individual laminate. General solution to the assembled state equation is then obtained according to the matrix theory. Taking account of the continuity conditions at the interfaces of all the adjacent lamina, a relationship between state variables at the top and bottom surfaces of the beam is established through a global transfer matrix. After incorporating the boundary conditions at these two surfaces, an eigenvalue equation for static problem is then derived. Numerical examples are presented, through which the accuracy and convergence characteristics of the present method are investigated. It is shown that the present method is of excellent efficiency for laminated composite thick beams subjected to arbitrary end supporting conditions.

TIME DOMAIN DIAKOPTIC ANALYSIS BASED ON REDUCED-ORDER STATE EQUATIONS

2007 ◽  
Vol 17 (10) ◽  
pp. 3625-3631 ◽  
Author(s):  
MIHAI IORDACHE ◽  
LUCIA DUMITRIU
Keyword(s):  
Analog Circuits ◽  
Large Scale ◽  
State Equation ◽  
The State ◽  
State Variables ◽  
State Equations ◽  
Integration Algorithm ◽  
Reduced Order ◽  
Decomposition Procedure ◽  
Minimum Number

In this paper we present some new tearing techniques to systematically formulate the state equations in symbolic normal-form for linear and/or nonlinear time-invariant large-scale analog circuits. The excess elements of the first and of the second kind are unitarily treated in order to allow a symbolic representation of the circuit with a minimum number of state variables. A procedure to reduce the state equation number of each subcircuit is also presented. The reduced-order is based on an implicit integration algorithm and on the successive elimination of the selected state variables. Examples are given to illustrate the decomposition procedure, the assignment of the connection sources and the reduced-order technique.

Robust attitude control of the three-dimensional unknown chaotic satellite system

2021 ◽  
pp. 014233122110561
Author(s):  
Muhammad Shafiq ◽  
Israr Ahmad ◽  
O Abdullah Almatroud ◽  
M Mossa Al-Sawalha
Keyword(s):  
Attitude Control ◽  
Closed Loop ◽  
Three Dimensional ◽  
Adaptive Controller ◽  
The State ◽  
Feedback Gain ◽  
State Variables ◽  
Nonlinear Controller ◽  
Model Uncertainties ◽  
Control Effort

This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

Non-iterative evaluation of multiphase thermal compliances in bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 13-19 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Bond Graph ◽  
The State ◽  
Refrigeration Cycle ◽  
State Variables ◽  
Unfinished Business ◽  
Bond Graphs ◽  
State Equations ◽  
Efficient Simulation ◽  
Multiple Phase ◽  
Iterative Evaluation

The practical use of bond graphs to organize the efficient simulation of multiple-phase thermodynamic systems is perhaps the most significant piece of unfinished business regarding the evolution of bond graphs. The most widely recognized form for these cases, called the pseudo bond graph, dictates particular causalities that require iteration, assuming the use of available state equations. This paper shows how the alternative convection bond graphs can direct non-iterative evaluation of state properties of multiphase thermal compliances. The state variables of a compliance become temperature, mass and volume. A refrigeration cycle is used as an example.

Development of a Robust Nonlinear Observer for a Single-Link Flexible Manipulator

2004 ◽  
Author(s):  
Nabil G. Chalhoub ◽  
Giscard A. Kfoury
Keyword(s):  
Sliding Mode ◽  
Initial Conditions ◽  
The State ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Flexible Manipulator ◽  
State Variables ◽  
State Equations ◽  
On Line ◽  
Simulation Results

Accurate measurements of all the state variables of a given system are often not available due to the high cost of sensors, the lack of space to mount the transducers or the hostile environment in which the sensors must be located. The purpose of this study is to design a robust sliding mode observer that is capable of accurately estimating the state variables of the system in the presence of disturbances and model uncertainties. It should be emphasized that the proposed observer design can handle state equations expressed in the general form. The performance of the nonlinear observer is assessed herein by examining its capability of predicting the rigid and flexible motions of a compliant beam that is connected to a revolute joint. The simulation results demonstrate the ability of the observer in accurately estimating the state variables of the system in the presence of structured uncertainties and under different initial conditions between the observer and the plant. Moreover, they illustrate the deterioration in the performance of the observer when subjected to unstructured uncertainties of the system. Furthermore, the nonlinear observer was successfully implemented to provide on-line estimates of the state variables for two model-based controllers. The simulation results show minimal deterioration in the closed-loop response of the system stemming from the usage of estimated rather than exact state variables in the computation of the control signals.

scholarly journals Multi-Cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space

2019 ◽  
Author(s):  
Michaelle N Mayalu ◽  
Min-Cheol Kim ◽  
Harry Asada
Keyword(s):  
Nonlinear Dynamics ◽  
Single Cell ◽  
State Variables ◽  
Computationally Efficient ◽  
State Equations ◽  
Cell Dynamics ◽  
Independent State ◽  
Collective Behaviors ◽  
Highly Nonlinear ◽  
Multiple Cells

AbstractCells interacting through an extracellular matrix (ECM) exhibit emergent behaviors resulting from collective intercellular interaction. In wound healing and tissue development, characteristic compaction of ECM gel is induced by multiple cells that generate tensions in the ECM fibers and coordinate their actions with other cells. Computational prediction of collective cell-ECM interaction based on first principles is highly complex especially as the number of cells increase. Here, we introduce a computationally-efficient method for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3-D ECM fiber network. The key enabling technique is superposition of single cell computational models to predict multicellular behaviors. While cell-ECM interactions are highly nonlinear, they can be linearized accurately with a unique method, termed Dual-Faceted Linearization. This method recasts the original nonlinear dynamics in an augmented space where the system behaves more linearly. The independent state variables are augmented by combining auxiliary variables that inform nonlinear elements involved in the system. This computational method involves a) expressing the original nonlinear state equations with two sets of linear dynamic equations b) reducing the order of the augmented linear system via principal component analysis and c) superposing individual single cell-ECM dynamics to predict collective behaviors of multiple cells. The method is computationally efficient compared to original nonlinear dynamic simulation and accurate compared to traditional Taylor expansion linearization. Furthermore, we reproduce reported experimental results of multi-cell induced ECM compaction.Author summaryCollective behaviors of multiple cells interacting through an ECM are prohibitively complex to predict with a mechanistic computational model due to its highly nonlinear dynamics and high dimensional space. We introduce a methodology where nonlinear dynamics of single cells are superposed to predict collective multi-cellular behaviors through a developed linearization method. We represent nonlinear single cell dynamics with linear state equations by augmenting the independent state variables with a set of auxiliary variables. We then transform the linear augmented state equations to a low-dimensional latent model and superpose the linear latent models of individual cells to predict collective behaviors that emerge from multi-cellular interactions. The method successfully reproduced experimental results of cell-induced ECM compaction.

Opponent Center-Surround Contrast: Colour to Grey Conversion

2020 ◽  
Vol 2020 (1) ◽  
pp. 105-108
Author(s):  
Ali Alsam
Keyword(s):  
Evolutionary Algorithms ◽  
Three Dimensional ◽  
The State ◽  
Colour Space ◽  
Vision Science ◽  
State Of Art ◽  
Over Time

Vision is the science that informs us about the biological and evolutionary algorithms that our eyes, opticnerves and brains have chosen over time to see. This article is an attempt to solve the problem of colour to grey conversion, by borrowing ideas from vision science. We introduce an algorithm that measures contrast along the opponent colour directions and use the results to combine a three dimensional colour space into a grey. The results indicate that the proposed algorithm competes with the state of art algorithms.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

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