To Solve the Load of Beam by Shearing Force Diagram and Bending Moment Diagram - Reverse Thinking in Strength of Materials

2014 ◽  
Vol 488-489 ◽  
pp. 546-549
Author(s):  
Heng Wen Zhang ◽  
Yue Shen ◽  
Sen Wei Zhang
Keyword(s):  
Inverse Problem ◽  
Bending Moment ◽  
Forward Problem ◽  
Load Case ◽  
Shearing Force ◽  
Strength Of Materials ◽  
Force Diagram ◽  
The Given

The paper has a discussion of forward problem and inverse problem for beams in strength of materials. Known load case of a beam can certainly determine its shearing force diagram and bending moment diagram, but conversely, there may be a variety of statically determinate or statically indeterminate constraint conditions. Furthermore, the solution from statically indeterminate constraint conditions doesnt agree with the given shearing force diagram and bending moment diagram in a general way.

DIRECT INVERSION OF TRANSMISSION SYNTHETIC SEISMOGRAMS

Geophysics ◽  
1978 ◽  
Vol 43 (5) ◽  
pp. 886-898 ◽  
Author(s):  
D. Loewenthal ◽  
P. R. Gutowski ◽  
S. Treitel
Keyword(s):  
Inverse Problem ◽  
Forward Problem ◽  
Direct Inversion ◽  
Homogeneous Half Space ◽  
Incident Plane ◽  
Free Case ◽  
Levinson Algorithm ◽  
Iterative Inversion ◽  
Inversion Techniques ◽  
The Given

Seismograms are routinely used to extract information about the internal structure of the subsurface. The basic philosophy is to idealize the earth with a simple model characterized by resolvable parameters. Further, we assume that the seismograms obey simple mathematical relations, such as the wave equation, and that these seismograms are uniquely determined by the given parameters. The computation of seismograms for a given model whose parameters are specified gives rise to the “forward problem”. The determination of the parameters of the model from the seismogram generally constitutes the “inverse problem”. While the forward problem is often relatively simple, the inverse problem tends to be much more involved. One of the few cases for which the inverse problem has a simple direct solution is given for a model consisting of a homogeneous one‐dimensional layered medium. The layers overlie a homogeneous half‐space, and are excited by a normally incident plane wave. Such direct solutions to the inverse problem are in contrast to the iterative inversion techniques of the Gilbert‐Backus type. We have chosen to treat the inverse problem for the seismogram escaping into the homogeneous substratum, i.e., the transmission seismogram. We do so because this time series is a simple autoregressive, or all‐pole process. The problem is studied both with and without white noise. The Wiener‐Levinson algorithm has been found to be well suited for the direct inversion of the noise‐free case, while the “maximum entropy” algorithm is generally more appropriate for noisy data. Numerical examples serve to clarify and illustrate these points.

Framework for Flaw Detection: Application to Dynamic Crack Detection in Flat Membranes

2008 ◽  
Author(s):  
Daniel Rabinovich ◽  
Dan Givoli ◽  
Shmuel Vigdergauz
Keyword(s):  
Inverse Problem ◽  
Crack Detection ◽  
Flexible Structures ◽  
Flaw Detection ◽  
Forward Problem ◽  
Dynamic Crack ◽  
Computational Framework ◽  
Time Harmonic ◽  
Present Context ◽  
Flat Membranes

A computational framework is developed for the detection of flaws in flexible structures. The framework is based on posing the detection problem as an inverse problem, which requires the solution of many forward problems. Each forward problem is associated with a known flaw; an appropriate cost functional evaluates the quality of each candidate flaw based on the solution of the corresponding forward problem. On the higher level, the inverse problem is solved by a global optimization algorithm. The performance of the computational framework is evaluated by considering the detectability of various types of flaws. In the present context detectability is defined by introducing a measure of the distance between the sought flaw and trial flaws in the space of the parameters characterizing the configuration of the flaw. The framework is applied to crack detection in flat membranes subjected to time-harmonic and transient excitations. The detectability of cracks is compared for these two cases.

scholarly journals Adjoint Numerical Method for a Multiphysical Inverse Problem of Two-Phase Well Testing in Petroleum Reservoirs

2021 ◽  
Vol 2090 (1) ◽  
pp. 012139
Author(s):  
OA Shishkina ◽  
I M Indrupskiy
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Objective Function ◽  
Petroleum Reservoirs ◽  
Forward Problem ◽  
Adjoint Equations ◽  
Well Testing ◽  
Adjoint Methods ◽  
Two Phase ◽  
Gradient Calculation

Abstract Inverse problem solution is an integral part of data interpretation for well testing in petroleum reservoirs. In case of two-phase well tests with water injection, forward problem is based on the multiphase flow model in porous media and solved numerically. The inverse problem is based on a misfit or likelihood objective function. Adjoint methods have proved robust and efficient for gradient calculation of the objective function in this type of problems. However, if time-lapse electrical resistivity measurements during the well test are included in the objective function, both the forward and inverse problems become multiphysical, and straightforward application of the adjoint method is problematic. In this paper we present a novel adjoint algorithm for the inverse problems considered. It takes into account the structure of cross dependencies between flow and electrical equations and variables, as well as specifics of the equations (mixed parabolic-hyperbolic for flow and elliptic for electricity), numerical discretizations and grids, and measurements in the inverse problem. Decomposition is proposed for the adjoint problem which makes possible step-wise solution of the electric adjoint equations, like in the forward problem, after which a cross-term is computed and added to the right-hand side of the flow adjoint equations at this timestep. The overall procedure provides accurate gradient calculation for the multiphysical objective function while preserving robustness and efficiency of the adjoint methods. Example cases of the adjoint gradient calculation are presented and compared to straightforward difference-based gradient calculation in terms of accuracy and efficiency.

Shearing force and bending moment

1990 ◽  
pp. 10-20
Author(s):  
D.H. Bacon ◽  
R.C. Stephens
Keyword(s):  
Bending Moment ◽  
Shearing Force

ON THE ADIABATICITY OF ACOUSTIC PROPAGATION THROUGH NONGRADUAL OCEAN STRUCTURES

2001 ◽  
Vol 09 (02) ◽  
pp. 359-365 ◽  
Author(s):  
E. C. SHANG ◽  
Y. Y. WANG ◽  
T. F. GAO
Keyword(s):  
Inverse Problem ◽  
Shallow Water ◽  
Acoustic Field ◽  
Solitary Waves ◽  
Sound Propagation ◽  
Acoustic Propagation ◽  
Forward Problem ◽  
Internal Solitary Waves ◽  
New Criterion

To assess the adiabaticity of sound propagation in the ocean is very important for acoustic field calculating (forward problem) and tomographic retrieving(inverse problem). Most of the criterion in the literature is too restrictive, specially for the nongradual ocean structures. A new criterion of adiabaticity is suggested in this paper. It works for nongradual ocean structures such as front and internal solitary waves in shallow-water.

scholarly journals Thrust and bending moment of rigid piles subjected to moving soil

2010 ◽  
Vol 47 (2) ◽  
pp. 180-196 ◽  
Author(s):  
Wei Dong Guo ◽  
H. Y. Qin
Keyword(s):  
Current Model ◽  
Bending Moment ◽  
Soil Movement ◽  
Model Pile ◽  
Experimental Apparatus ◽  
Lateral Soil Movement ◽  
Laterally Loaded ◽  
The Given ◽  
Maximum Thrust

An experimental apparatus was developed to investigate the behaviour of vertically loaded free-head piles in sand undergoing lateral soil movement (wf). A large number of tests have been conducted to date. Presented here are 14 typical model pile tests concerning two diameters, two vertical pile loading levels, and varying sliding depths with the movement wf driven by a triangular loading block. Results are provided for driving force as well as for induced shear force (T), bending moment (M), and deflection ( y) along the piles with wf / normalized sliding depth. The tests enable simple expressions to be proposed, drawn from the theory for a laterally loaded pile. The new expressions well capture the evolution of M, T, and y with soil movement observed in current model tests, and the three to five times difference in maximum bending moment (Mmax) from the two modes of loading. They further offer a good estimate of Mmax for eight in situ pile tests and one centrifuge test pile. The study quantifies the sliding resistance offered by a pile for the given wf profiles, pile location (relative to the boundary), and vertical load. It establishes the linear correlation between the maximum thrust (resistance T) and Mmax, regardless of the magnitudes of wf.

The Study of FEM for Internal Force Analysis of the Sluice Structure

2011 ◽  
Vol 71-78 ◽  
pp. 3275-3279
Author(s):  
Xiao Na Li ◽  
Tong Chun Li ◽  
Yuan Ding
Keyword(s):  
Cross Section ◽  
Bending Moment ◽  
Internal Force ◽  
Force Balance ◽  
Shearing Force ◽  
Force Analysis ◽  
Reconstruction Project ◽  
Unit Stress ◽  
Reinforcement Design

This paper takes a sluice reconstruction project as an example. The constraint internal force, the related axis force, bending moment, and shearing force at the corresponding section are solved according to the unit stress and internal force balance. Furthermore, technology of mesh auto-generation in cross-section is utilized to plot the internal force graph of the structure directly, which will provide reference for reinforcement design and make it more convenient.

Learning solutions to the source inverse problem of wave equations using LS-SVM

2019 ◽  
Vol 27 (5) ◽  
pp. 657-669 ◽  
Author(s):  
Ziku Wu ◽  
Chang Ding ◽  
Guofeng Li ◽  
Xiaoming Han ◽  
Juan Li
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Support Vector Machines ◽  
Wave Equations ◽  
Source Term ◽  
Initial Conditions ◽  
Support Vector ◽  
Vector Machines ◽  
Robustness To Noise ◽  
The Given

Abstract A method based on least squares support vector machines (LS-SVM) is proposed to solve the source inverse problem of wave equations. Contrary to the most existing methods, the proposed method provides a closed form approximate solution which satisfies the boundary conditions and the initial conditions. The proposed method can recover the unknown source term with the given additional conditions. Furthermore, it has reasonable robustness to noise. Numerical results show the proposed method can be used to solve the source inverse problem of wave equations.

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