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Structural Mechanics
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Features of Structural Mechanics

Cross-Sectional Properties

  • Performs both symbolic and numeric calculations of cross-sectional properties such as areas, centroids, and moments of inertia
  • Includes standard cross sections including rectangular sections, circle and ellipse sectors, right triangles, and parallelograms
  • Allows the introduction of user-defined domain objects
  • Computes moments of inertia and location of centroid for translated and/or rotated cross sections
  • Numerically calculates the area, centroid, and moment of inertia of any polygon
  • Generates graphical representations of cross sections and marks dimensions on cross-sectional plots

Beam Stress Analysis

  • Determines closed-form solutions for Timoshenko beams with circular, elliptical, equilateral-triangular, and rectangular cross sections
  • Calculates the bending function, bending stresses, and center-of-line deflection
  • Generates plots of bent beams

Torsional Analysis

  • Calculates the twist, torsional rigidity, stress function, displacements, and stresses in closed form
  • Includes examples for torsional analysis of circular, elliptical, equilateral-triangular, rectangular, circle-sector, and semicircular cross sections
  • Provides torsional rigidities for narrow-bar cross sections and hollow concentric circular sections
  • Computes stress functions using complex polynomials
  • Plots twisted beams and rotated cross sections

Finite Element Analysis

  • Covers one- and two-dimensional finite element method
  • Constructs interpolation (shape) functions
  • Includes Lagrange, Hermite, and serendipity elements
  • Solves plane elasticity problems for both isotropic and anisotropic materials
  • Provides intermediate steps for FEA training and educational purposes
  • Generates mesh, using a triangulation scheme and isoparametric formulation
  • Includes graphical tools for plotting mesh and deformed mesh

Analysis of Stress

  • Constructs and plots Mohr's circles
  • Calculates the principal stresses, principal stress directions, and stress invariants from the stress state at a point
  • Calculates the normal stress and shear components for given principal stresses and direction
  • Includes failure theories such as maximum shear stress theory, distortion energy theory, and maximum normal stress theory

Equations of Elasticity

  • Allows manipulation of governing elasticity equations in Cartesian, polar, and spherical coordinates
  • Calculates strain-displacement relationships
  • Calculates stress-strain relationships
  • Calculates equations of equilibrium
  • Calculates elastodynamics equations
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