It is adopted from the book :

**Advanced Mathematics and Mechanics Applications Using MATLAB, 3rd Edition**

**Download the chapter from here :**

Bending Analysis Of Beams Of General Cross Section.pdf

**Download the free m files here :**

m files

Started by
unique33
, Jun 28 2007 09:52 PM

8 replies to this topic

Posted 28 June 2007 - 09:52 PM

Can any one help to convert this MATLAB programs to Cplua ?

It is adopted from the book :

**Advanced Mathematics and Mechanics Applications Using MATLAB, 3rd Edition **

**Download the chapter from here :**

Bending Analysis Of Beams Of General Cross Section.pdf

**Download the free m files here :**

m files

It is adopted from the book :

Bending Analysis Of Beams Of General Cross Section.pdf

m files

Posted 28 June 2007 - 10:20 PM

here is the index of the book :

[If any one is MATLAB expert and want to help converting and need any of the specific chapter let me know , specialy the Appendix]

in such a case send me private message.

-------------------------------------------------------------------------------------

1 Introduction

1.1 MATLAB:A Tool for Engineering Analysis

1.2 MATLAB Commands and Related Reference Materials

1.3 Example Problemon Financial Analysis

1.4 Computer Code and Results

1.4.1 Computer Output

1.4.2 Discussion of the MATLAB Code

1.4.3 Code for Financial Problem

-------------------------------------------------------------------------------------

2 Elementary Aspects of MATLAB Graphics

2.1 Introduction

2.2 Overviewof Graphics

2.3 Example Comparing Polynomial and Spline Interpolation

2.4 Conformal Mapping Example

2.5 Nonlinear Motion of a Damped Pendulum

2.6 A Linear Vibration Model

2.7 Example of Waves in an Elastic String

2.8 Properties of Curves and Surfaces

2.8.1 Curve Properties

2.8.2 Surface Properties

2.8.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

3 Summary of Concepts fromLinear Algebra

3.1 Introduction

3.2 Vectors, Norms, Linear Independence, and Rank

3.3 Systems of Linear Equations, Consistency, and Least Squares Ap-

proximation

3.4 Applications of Least Squares Approximation

3.4.1 A Membrane De?ection Problem

3.4.2 Mixed Boundary Value Problem for a Function Harmonic

Inside a Circular Disk

3.4.3 Using Rational Functions to Conformally Map a Circular

Disk onto a Square

3.5 Eigenvalue Problems

3.5.1 Statement of the Problem

3.5.2 Application to Solution of Matrix Differential Equations

3.5.3 The Structural Dynamics Equation

3.6 Computing Natural Frequencies for a Rectangular Membrane

3.7 Column Space, Null Space, Orthonormal Bases, and SVD

3.8 Computation Time to Run a MATLAB Program

-------------------------------------------------------------------------------------

4 Methods for Interpolation and Numerical Differentiation

4.1 Concepts of Interpolation

4.2 Interpolation, Differentiation, and Integration by Cubic Splines

4.2.1 Computing the Length and Area Bounded by a Curve

4.2.2 Example: Length and Enclosed Area for a Spline Curve

4.2.3 Generalizing the Intrinsic Spline Function in MATLAB

4.2.4 Example: A Spline Curve with Several Parts and Corners

4.3 Numerical Differentiation Using Finite Differences

4.3.1 Example: Programto Derive Difference Formulas

-------------------------------------------------------------------------------------

5 Gauss Integration with Geometric Property Applications

5.1 Fundamental Concepts and Intrinsic Integration Tools in MATLAB

5.2 Concepts of Gauss Integration

5.3 Comparing Results fromGauss Integration and Function QUADL

5.4 Geometrical Properties of Areas and Volumes

5.4.1 Area Property Program

5.4.2 ProgramAnalyzing Volumes of Revolution

5.5 Computing Solid Properties Using Triangular Surface Elements and

Using Symbolic Math

5.6 Numerical and Symbolic Results for the Example

5.7 Geometrical Properties of a Polyhedron

5.8 Evaluating Integrals Having Square Root Type Singularities

5.8.1 ProgramListing

5.9 Gauss Integration of a Multiple Integral

5.9.1 Example: Evaluating a Multiple Integral

-------------------------------------------------------------------------------------

6 Fourier Series and the Fast Fourier Transform

6.1 De?nitions and Computation of Fourier Coef?cients

6.1.1 Trigonometric Interpolation and the Fast Fourier Transform

6.2 Some Applications

6.2.1 Using the FFT to Compute Integer Order Bessel Functions

6.2.2 Dynamic Response of a Mass on an Oscillating Foundation

6.2.3 General Programto Plot Fourier Expansions

-------------------------------------------------------------------------------------

7 Dynamic Response of Linear Second Order Systems

7.1 Solving the Structural Dynamics Equations for Periodic Forces

7.1.1 Application to Oscillations of a Vertically Suspended Cable

7.2 Direct Integration Methods

7.2.1 Example on Cable Response by Direct Integration

-------------------------------------------------------------------------------------

8 Integration of Nonlinear Initial Value Problems

8.1 General Concepts on Numerical Integration of Nonlinear Matrix Dif-

ferential Equations

8.2 Runge-Kutta Methods and the ODE45 Integrator Provided in MAT-

LAB

8.3 Step-size Limits Necessary to Maintain Numerical Stability

8.4 Discussion of Procedures to Maintain Accuracy by Varying Integra-

tion Step-size

8.5 Example on Forced Oscillations of an Inverted Pendulum

8.6 Dynamics of a Spinning Top

8.7 Motion of a Projectile

8.8 Example on Dynamics of a Chain with Speci?ed End Motion

8.9 Dynamics of an Elastic Chain

-------------------------------------------------------------------------------------

9 Boundary Value Problems for Partial Differential Equations

9.1 Several Important Partial Differential Equations

9.2 Solving the Laplace Equation inside a Rectangular Region

9.3 The Vibrating String

9.4 Force Moving on an Elastic String

9.4.1 Computer Analysis

9.5 Waves in Rectangular or Circular Membranes

9.5.1 Computer Formulation

9.5.2 Input Data for Programmembwave

9.6 Wave Propagation in a Beam with an Impact Moment Applied to

One End

9.7 Forced Vibration of a Pile Embedded in an Elastic Medium

9.8 Transient Heat Conduction in a One-Dimensional Slab

9.9 Transient Heat Conduction in a Circular Cylinder with Spatially Vary-

ing Boundary Temperature

9.9.1 ProblemFormulation

9.9.2 Computer Formulation

9.10 Torsional Stresses in a Beamof Rectangular Cross Section

-------------------------------------------------------------------------------------

10 Eigenvalue Problems and Applications

10.1 Introduction

10.2 Approximation Accuracy in a Simple Eigenvalue Problem

10.3 Stress Transformation and Principal Coordinates

10.3.1 Principal Stress Program

10.3.2 Principal Axes of the Inertia Tensor

10.4 Vibration of Truss Structures

10.4.1 Truss Vibration Program

10.5 Buckling of Axially Loaded Columns

10.5.1 Example for a Linearly Tapered Circular Cross Section

10.5.2 Numerical Results

10.6 Accuracy Comparison for Euler Beam Natural Frequencies by Finite

Element and Finite Difference Methods

10.6.1 Mathematical Formulation

10.6.2 Discussion of the Code

10.6.3 Numerical Results

10.7 Vibration Modes of an Elliptic Membrane

10.7.1 Analytical Formulation

10.7.2 Computer Formulation

-------------------------------------------------------------------------------------

11 Bending Analysis of Beams of General Cross Section

11.1 Introduction

11.1.1 Analytical Formulation

11.1.2 Programto Analyze Beams of General Cross Section

11.1.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

12 Applications of Analytic Functions

12.1 Properties of Analytic Functions

12.2 De?nition of Analyticity

12.3 Series Expansions

12.4 Integral Properties

12.4.1 Cauchy Integral Formula

12.4.2 Residue Theorem

12.5 Physical Problems Leading to Analytic Functions

12.5.1 Steady-State Heat Conduction

12.5.2 Incompressible Inviscid Fluid Flow

12.5.3 Torsion and Flexure of Elastic Beams

12.5.4 Plane Elastostatics

12.5.5 Electric Field Intensity

12.6 Branch Points and Multivalued Behavior

12.7 Conformal Mapping and Harmonic Functions

12.8 Mapping onto the Exterior or the Interior of an Ellipse

12.8.1 ProgramOutput and Code

12.9 Linear Fractional Transformations

12.9.1 ProgramOutput and Code

12.10 Schwarz-Christoffel Mapping onto a Square

12.10.1 ProgramOutput and Code

12.11 Determining Harmonic Functions in a Circular Disk

12.11.1 Numerical Results

12.11.2 ProgramOutput and Code

12.12 Inviscid Fluid Flow around an Elliptic Cylinder

12.12.1 ProgramOutput and Code

12.13 Torsional Stresses in a BeamMapped onto a Unit Disk

12.13.1 ProgramOutput and Code

12.14 Stress Analysis by the Kolosov-Muskhelishvili Method

12.14.1 ProgramOutput and Code

12.14.2 Stressed Plate with an Elliptic Hole

12.14.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

13 Nonlinear Optimization Applications

13.1 Basic Concepts

13.2 Initial Angle for a Projectile

13.3 Fitting Nonlinear Equations to Data

13.4 Nonlinear De?ections of a Cable

13.5 Quickest Time Descent Curve (the Brachistochrone)

13.6 Determining the Closest Points on Two Surfaces

13.6.1 Discussion of the Computer Code

-------------------------------------------------------------------------------------

**A List of MATLAB Routines with Descriptions**

B Selected Utility and Application Functions

References

-------------------------------------------------------------------------------------

[If any one is MATLAB expert and want to help converting and need any of the specific chapter let me know , specialy the Appendix]

in such a case send me private message.

-------------------------------------------------------------------------------------

1 Introduction

1.1 MATLAB:A Tool for Engineering Analysis

1.2 MATLAB Commands and Related Reference Materials

1.3 Example Problemon Financial Analysis

1.4 Computer Code and Results

1.4.1 Computer Output

1.4.2 Discussion of the MATLAB Code

1.4.3 Code for Financial Problem

-------------------------------------------------------------------------------------

2 Elementary Aspects of MATLAB Graphics

2.1 Introduction

2.2 Overviewof Graphics

2.3 Example Comparing Polynomial and Spline Interpolation

2.4 Conformal Mapping Example

2.5 Nonlinear Motion of a Damped Pendulum

2.6 A Linear Vibration Model

2.7 Example of Waves in an Elastic String

2.8 Properties of Curves and Surfaces

2.8.1 Curve Properties

2.8.2 Surface Properties

2.8.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

3 Summary of Concepts fromLinear Algebra

3.1 Introduction

3.2 Vectors, Norms, Linear Independence, and Rank

3.3 Systems of Linear Equations, Consistency, and Least Squares Ap-

proximation

3.4 Applications of Least Squares Approximation

3.4.1 A Membrane De?ection Problem

3.4.2 Mixed Boundary Value Problem for a Function Harmonic

Inside a Circular Disk

3.4.3 Using Rational Functions to Conformally Map a Circular

Disk onto a Square

3.5 Eigenvalue Problems

3.5.1 Statement of the Problem

3.5.2 Application to Solution of Matrix Differential Equations

3.5.3 The Structural Dynamics Equation

3.6 Computing Natural Frequencies for a Rectangular Membrane

3.7 Column Space, Null Space, Orthonormal Bases, and SVD

3.8 Computation Time to Run a MATLAB Program

-------------------------------------------------------------------------------------

4 Methods for Interpolation and Numerical Differentiation

4.1 Concepts of Interpolation

4.2 Interpolation, Differentiation, and Integration by Cubic Splines

4.2.1 Computing the Length and Area Bounded by a Curve

4.2.2 Example: Length and Enclosed Area for a Spline Curve

4.2.3 Generalizing the Intrinsic Spline Function in MATLAB

4.2.4 Example: A Spline Curve with Several Parts and Corners

4.3 Numerical Differentiation Using Finite Differences

4.3.1 Example: Programto Derive Difference Formulas

-------------------------------------------------------------------------------------

5 Gauss Integration with Geometric Property Applications

5.1 Fundamental Concepts and Intrinsic Integration Tools in MATLAB

5.2 Concepts of Gauss Integration

5.3 Comparing Results fromGauss Integration and Function QUADL

5.4 Geometrical Properties of Areas and Volumes

5.4.1 Area Property Program

5.4.2 ProgramAnalyzing Volumes of Revolution

5.5 Computing Solid Properties Using Triangular Surface Elements and

Using Symbolic Math

5.6 Numerical and Symbolic Results for the Example

5.7 Geometrical Properties of a Polyhedron

5.8 Evaluating Integrals Having Square Root Type Singularities

5.8.1 ProgramListing

5.9 Gauss Integration of a Multiple Integral

5.9.1 Example: Evaluating a Multiple Integral

-------------------------------------------------------------------------------------

6 Fourier Series and the Fast Fourier Transform

6.1 De?nitions and Computation of Fourier Coef?cients

6.1.1 Trigonometric Interpolation and the Fast Fourier Transform

6.2 Some Applications

6.2.1 Using the FFT to Compute Integer Order Bessel Functions

6.2.2 Dynamic Response of a Mass on an Oscillating Foundation

6.2.3 General Programto Plot Fourier Expansions

-------------------------------------------------------------------------------------

7 Dynamic Response of Linear Second Order Systems

7.1 Solving the Structural Dynamics Equations for Periodic Forces

7.1.1 Application to Oscillations of a Vertically Suspended Cable

7.2 Direct Integration Methods

7.2.1 Example on Cable Response by Direct Integration

-------------------------------------------------------------------------------------

8 Integration of Nonlinear Initial Value Problems

8.1 General Concepts on Numerical Integration of Nonlinear Matrix Dif-

ferential Equations

8.2 Runge-Kutta Methods and the ODE45 Integrator Provided in MAT-

LAB

8.3 Step-size Limits Necessary to Maintain Numerical Stability

8.4 Discussion of Procedures to Maintain Accuracy by Varying Integra-

tion Step-size

8.5 Example on Forced Oscillations of an Inverted Pendulum

8.6 Dynamics of a Spinning Top

8.7 Motion of a Projectile

8.8 Example on Dynamics of a Chain with Speci?ed End Motion

8.9 Dynamics of an Elastic Chain

-------------------------------------------------------------------------------------

9 Boundary Value Problems for Partial Differential Equations

9.1 Several Important Partial Differential Equations

9.2 Solving the Laplace Equation inside a Rectangular Region

9.3 The Vibrating String

9.4 Force Moving on an Elastic String

9.4.1 Computer Analysis

9.5 Waves in Rectangular or Circular Membranes

9.5.1 Computer Formulation

9.5.2 Input Data for Programmembwave

9.6 Wave Propagation in a Beam with an Impact Moment Applied to

One End

9.7 Forced Vibration of a Pile Embedded in an Elastic Medium

9.8 Transient Heat Conduction in a One-Dimensional Slab

9.9 Transient Heat Conduction in a Circular Cylinder with Spatially Vary-

ing Boundary Temperature

9.9.1 ProblemFormulation

9.9.2 Computer Formulation

9.10 Torsional Stresses in a Beamof Rectangular Cross Section

-------------------------------------------------------------------------------------

10 Eigenvalue Problems and Applications

10.1 Introduction

10.2 Approximation Accuracy in a Simple Eigenvalue Problem

10.3 Stress Transformation and Principal Coordinates

10.3.1 Principal Stress Program

10.3.2 Principal Axes of the Inertia Tensor

10.4 Vibration of Truss Structures

10.4.1 Truss Vibration Program

10.5 Buckling of Axially Loaded Columns

10.5.1 Example for a Linearly Tapered Circular Cross Section

10.5.2 Numerical Results

10.6 Accuracy Comparison for Euler Beam Natural Frequencies by Finite

Element and Finite Difference Methods

10.6.1 Mathematical Formulation

10.6.2 Discussion of the Code

10.6.3 Numerical Results

10.7 Vibration Modes of an Elliptic Membrane

10.7.1 Analytical Formulation

10.7.2 Computer Formulation

-------------------------------------------------------------------------------------

11 Bending Analysis of Beams of General Cross Section

11.1 Introduction

11.1.1 Analytical Formulation

11.1.2 Programto Analyze Beams of General Cross Section

11.1.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

12 Applications of Analytic Functions

12.1 Properties of Analytic Functions

12.2 De?nition of Analyticity

12.3 Series Expansions

12.4 Integral Properties

12.4.1 Cauchy Integral Formula

12.4.2 Residue Theorem

12.5 Physical Problems Leading to Analytic Functions

12.5.1 Steady-State Heat Conduction

12.5.2 Incompressible Inviscid Fluid Flow

12.5.3 Torsion and Flexure of Elastic Beams

12.5.4 Plane Elastostatics

12.5.5 Electric Field Intensity

12.6 Branch Points and Multivalued Behavior

12.7 Conformal Mapping and Harmonic Functions

12.8 Mapping onto the Exterior or the Interior of an Ellipse

12.8.1 ProgramOutput and Code

12.9 Linear Fractional Transformations

12.9.1 ProgramOutput and Code

12.10 Schwarz-Christoffel Mapping onto a Square

12.10.1 ProgramOutput and Code

12.11 Determining Harmonic Functions in a Circular Disk

12.11.1 Numerical Results

12.11.2 ProgramOutput and Code

12.12 Inviscid Fluid Flow around an Elliptic Cylinder

12.12.1 ProgramOutput and Code

12.13 Torsional Stresses in a BeamMapped onto a Unit Disk

12.13.1 ProgramOutput and Code

12.14 Stress Analysis by the Kolosov-Muskhelishvili Method

12.14.1 ProgramOutput and Code

12.14.2 Stressed Plate with an Elliptic Hole

12.14.3 ProgramOutput and Code

-------------------------------------------------------------------------------------

13 Nonlinear Optimization Applications

13.1 Basic Concepts

13.2 Initial Angle for a Projectile

13.3 Fitting Nonlinear Equations to Data

13.4 Nonlinear De?ections of a Cable

13.5 Quickest Time Descent Curve (the Brachistochrone)

13.6 Determining the Closest Points on Two Surfaces

13.6.1 Discussion of the Computer Code

-------------------------------------------------------------------------------------

B Selected Utility and Application Functions

References

-------------------------------------------------------------------------------------

Posted 29 June 2007 - 04:00 PM

Sorry I dont have MATLAB so I cant help (or may help if I understand the source).

Is there any document (not source code) for it?...

I will spend a lot of time time for it if youcan help me: how can I know the production of a chemical equation. (

Is there any document (not source code) for it?...

I will spend a lot of time time for it if youcan help me: how can I know the production of a chemical equation. (

Posted 29 June 2007 - 08:52 PM

I posted the link for documentation !Is there any document (not source code) for it?...

It is not only the source code , it contains the demonstrations ,...

In my mind you do not need MATLAB , you need the time , which unfortunately I do not have .Sorry I dont have MATLAB so I cant help (or may help if I understand the source).

Posted 01 July 2007 - 12:30 PM

Ok, I will try.

Posted 09 July 2007 - 06:25 PM

I have tried to using Mathlab compiler to gain C codes for some toolboxes and some M files. but unfortunately I found that Mathlab compiler is just a FUNNY F***ing JOKE! It will compile to C codes but for just ploting a very simple function like y=sin(x) in numeric mode(not using symbolic toolbox witch is not possible to compile) my computer takes about 1 minute to run the compiled C codes!(Pentium III @800MHz and 256MB of RAM).

So the best way for numerical solution is using Matlab algorithms to write your own program in CPLUA and using LNA . For symbolic solutions again use CPLUA and use CP CAS .

If you have plenty of time(1 year for example) use CPBasic !

So the best way for numerical solution is using Matlab algorithms to write your own program in CPLUA and using LNA . For symbolic solutions again use CPLUA and use CP CAS .

If you have plenty of time(1 year for example) use CPBasic !

Posted 10 July 2007 - 11:55 AM

You shouldn't be surprised at all, what do you expect from commercial (and expensive) software? Try Scilab instead. You will not find a true compiler, because there is no such a thing in all programs of this kind, but you will find the power of the OpenSource.I have tried to using Mathlab compiler to gain C codes for some toolboxes and some M files. but unfortunately I found that Mathlab compiler is just a FUNNY F***ing JOKE! It will compile to C codes but for just ploting a very simple function like y=sin(x) in numeric mode(not using symbolic toolbox witch is not possible to compile) my computer takes about 1 minute to run the compiled C codes!(Pentium III @800MHz and 256MB of RAM).

Posted 11 July 2007 - 01:43 PM

Yes, I agree with you. Scilab is a nice OpenSource program but unfortunately it isn't as plenary as Matlab is.

Matlab is big mistake in history of programming. It is a new record in low performance programming!

Matlab is big mistake in history of programming. It is a new record in low performance programming!

Posted 18 July 2007 - 11:29 PM

yes , you are right .

but just I need the code to be translated to Cplua .

I searched and I found this code on the net .

If anyone has better code so share it

but keep the goal : Cp**Lua Beam Analyser**

but just I need the code to be translated to Cplua .

I searched and I found this code on the net .

If anyone has better code so share it

but keep the goal : Cp

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