Structural Mechanics

## 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