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## Examples (40) |
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Try examples created by members of SMath community to see different features provided by application. Opened documents can be easily edited in order to test them or use with your own input data. |

Planetary gear with internal teeth Animation in SMath Studio shown by the example of planetary gear with internal teeth. Jacobi matrix and Jacobian Algorithm of Jacobi matrix generation and the definition of the Jacobian.
The user specifies a function to construct Jacobian matrix in the loop using partial derivatives.
The last step defines the functions to work with the result. All calculations are performs in symbols, with the possibility to get Symbolic and Numeric results of the algorithm. Beam Analysis Input Guide Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following:
1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection
2.) Calculates Support Reactions
3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin. Nonlinear systems of equations solving with Newton's method Newton's method of the nonlinear systems of equations solving. This algorithm can be used to solve standalone equation as well.
User specifies system of the equations, first approximations of the roots and the result accuracy.
While calculation Jacobi matrix is created.
Number of steps (iterations) of the While loop also displayed for the analysis purposes. Getting started with SMath Studio Interactive guide to make you familiar with basic features of SMath Studio (appr. 2h) Language-Integrated Query (Linq). Useful functions for working with sets. Generation of correlated random variable sets with normal distribution Generates correlated random variables from uncorrelated random variables with normal distribution Legendre polynomials solving Solving of Legendre polynomials defined by Rodrigues' formula.
User specifies a power of the polinomial to get it's roots.
Additionally represented graphs of first five Legendre functions. Hermite polynomials solving Solving of Hermite polynomials.
User specifies a power of the polinomial to get it's roots.
Additionally represented graphs of first five Hermite functions. Function of the matrix (Sylvester's formula) Computing the user-defined function of the matrix using Sylvester's formula.
Example also shows how to get the coefficients of matrix characteristic polynomial with Leverrie-Faddeev method. Numeric integration method (Simpson's rule) Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals.
User specifies function to integrate, interval and the number of iterations.
At the end of calculation program controls the result with a built-in numerical integration function. Embedded Plate calculations Embedded Plate calculation program. Plate is calculated under static loading. Creates a graphical representation and prepares specifications. Beam Analysis Sample-1 Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following:
1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection
2.) Calculates Support Reactions
3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin. Euclidean algorithm (calculating the GCD) Efficient method for computing the greatest common divisor (GCD), also known as the greatest common factor (GCF) or highest common factor (HCF). The algorithm is also called Euclid's algorithm.
User fills in two numbers to find out the GCD. This is a simple Numeric example, that uses While Loop inside. Arabic to Roman numeral conversion Algorithm for conversion Arabic numerals to Roman numerals.
User specifies a number using Arabic digits. Program shows a result of conversion in Roman numerals form. Fifth-order Runge–Kutta method with adaptive step Solution of ordinary differential equations using Fifth-order Runge–Kutta method with adaptive step.
User defines initial equation coefficients, a Cauchy problem (initial value problem), segment limits and calculations precision.
Program converts equation to the system of equations and starts evaluation with the Fifth-order Runge–Kutta method.
Algorithm automatically choose the optimal step of the iterations in respect to the specified accuracy.
After calculations program represents the graphs of numeric solution using cubic splines interpolation. Nonlinear equations solving with dichotomy method Nonlinear equations solving with dichotomy method.
User defines initial equation to proceed, calculation precision and the range.
Program returns root of the initial equation, result accuracy and number of iterations. Beam Analysis Sample-5 Analysis of Beam with any number of supports and with any type of loadings.The worksheet requires that the associated Plugin (Structural Beam Analysis Utililty Functions by Redem Legaspi Jr.) be downloaded and enabled from SMath Studio Extension Manager tool.The worksheet does the following:
1.) Plots Beam Diagram, Shear Diagram, Moment Diagram, Deflection
2.) Calculates Support Reactions
3.) Calculates Shear, Moment, and Deflection at any given point.Refer to 'Beam Analysis Input Guide.sm' on how to use the plugin. Beam load calculation bearing with two supports Calculation of the Beam load bearing with two supports to find stresses values of the supports.
Worksheet requires to specify any number of the Point and/or Uniform Loads.
Every input and output data supports values with Uniits. Computation of gravitation acceleration on the object's surface Example demonstrates a computation of gravitation acceleration on the Solar System astronomical object's surfaces.
Computation performed for eight Solar System planets and for the Sun. Beam Analysis Sample-7 Beam FEA with interactive preprocessor 2D horizontal beam finite element analysis with exact representation of trapezoidal distributed loads. Features an interactive preprocessor and graphic and tabular output Foundation calculations The program of calculation of monolithic reinforced concrete foundations. Calculates the concrete foundation under static loading of an arbitrary number of columns. Creates a graphical representation with the preparation of specifications and steel sampling costs. Solving Linear Systems of Equations with the Cholesky method Example for the solution of linear systems of equations with positiv definite coefficient matrix, via the Cholesky method Hesse matrix and Hessian Algorithm of Hesse matrix generation and the definition of the Hessian.
The user specifies a function to construct Hessian matrix in the loop using partial derivatives.
The last step defines the functions to work with the result. All calculations are performs in symbols, with the possibility to get Symbolic and Numeric results of the algorithm. Solve of tridiagonal system of equations The tridiagonal matrix algorithm (TDMA), also known as the Thomas algorithm, is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.
Example shows how to extract diagonals of the matrix and how to use it to calculate the result. Laguerre polynomials solving Solving of Laguerre polynomials.
User specifies a power of the polinomial to get it's roots.
Additionally represented graphs of first five Laguerre functions. Text region Fonts A collection of text regions with different font-families. 2D plots with hatch and fill This example demonstrates the usage of the snippets hatch and fill in 2D plots Beam Analysis Sample-3 Expansion of function to Maclaurin series Expansion of the user-defined function to Maclaurin series with a custom degree. Beam Analysis Sample-6 Steam engine Oscillating cylinder steam engine Beam Analysis Sample-2 Properties of generic polygons calculate properties of generic polygons:- perimeter- area- centroid- second moment of area- radii of gyration- elastic section modulus- plastic section modulus- orientation of principal axes of inertia- principal moments of inertia- radius of gyration about principal axes of inertia- shortcuts for easy plots- multilanguage[EN/IT] Colors of the rainbow Game to compose colors of the rainbow in correct order. Nonlinear equations solving with chord method Nonlinear equations solving with chord method.
User defines initial equation to proceed, calculation precision and the range.
Program returns root of the initial equation, result accuracy and number of iterations. Beam Analysis Sample-4 |