Delving Beyond Basic Physics

Finite Element Analysis (FEA)

FEA is a powerful numerical technique used to solve complex structural mechanics problems. Unlike direct stress calculations, FEA divides a body into smaller elements – typically triangles or quadrilaterals – and calculates stresses and strains within each element based on applied loads and material properties.

The simulation iteratively refines the mesh size until a desired level of accuracy is achieved. Key parameters include element type (linear vs. quadratic), mesh density, boundary conditions (fixed supports, displacement constraints), and material models (elastic, plastic, hyperelastic).

Δσ = Eε  (Simplified linear elastic FEA equation)

Computational Fluid Dynamics (CFD)

CFD involves simulating fluid flow using numerical methods. It’s based on the Navier-Stokes equations, which describe conservation of mass, momentum, and energy for viscous fluids.

The simulation discretizes the domain into a mesh and solves these equations numerically, typically employing techniques like Finite Volume Method (FVM) or Finite Element Method (FEM). Reynolds number is critical in determining flow characteristics.

ρ(∂v/∂t + v⋅∇v) = -∇p + μ∇²v  (Simplified Navier-Stokes equation)

Transient Heat Transfer

This focuses on simulating heat transfer processes where temperatures vary over time. It builds upon steady-state heat transfer principles but introduces the concept of temporal evolution.

Governing equations include Fourier's Law for conductive heat transfer, convection, and radiation. Numerical methods such as Finite Difference Method (FDM) are commonly used to solve these coupled partial differential equations.

q = -k∇T  (Fourier’s Law of Heat Conduction)

Multiphysics Simulation

Advanced simulations often combine multiple physics domains – for example, fluid-structure interaction (FSI), where the deformation of a solid structure affects the flow around it, or thermal-structural analysis, where temperature changes induce stresses in a material.

These multiphysics simulations require sophisticated coupling algorithms to exchange data between different solvers accurately. Careful consideration must be given to numerical stability and convergence criteria.

Frequently asked questions

Try it live

Everything above runs in your browser — open Bridge Structural Analysis and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.