stressanalyses

Stress analysis is the evaluation of how internal stresses distribute within a solid body under external loads, temperature changes, or other effects. It uses concepts from continuum mechanics, treating materials as continuous media and describing the state of stress with a stress tensor. Analyses can be elastic (reversible) or plastic (permanent), and may consider static or time-varying conditions.

Analytical methods solve the governing equations of equilibrium, compatibility, and constitutive relations for simple geometries and loading cases. Classic approaches include methods from strength of materials, Mohr’s circle, and closed-form solutions for beams, pressure vessels, and thin-walled sections. For more complex geometries, numerical methods are employed.

Numerical methods, notably the finite element method (FEM), discretize a structure into elements and solve for nodal displacements from which stresses are derived. Other techniques include boundary element methods and meshless methods. The analysis typically yields principal stresses, maximum shear stresses, and stress measures such as von Mises or Tresca equivalents, which are used to assess yield or failure under given material criteria.

Key considerations in stress analysis include material properties (elastic moduli, yield strength, hardening behavior), boundary conditions, load paths, and the presence of geometric discontinuities that cause stress concentrations. Analyses may be static or dynamic, and may address fatigue, thermal stresses, residual stresses, or nonlinear material behavior.

Applications span mechanical, civil, and aerospace engineering: from designing load-bearing components to performing failure investigations and reliability assessments. Validation often involves experiments such as strain gauges, photoelasticity, or digital image correlation to verify analytical or numerical predictions.