Langford Analytic · Knowledge Base
Non-Linear & Transient Analysis
How structural response changes when deformation alters geometry, materials yield, contact evolves or boundary conditions shift — covering geometric and material non-linearity, contact mechanics, nonlinear quasi-static response, incremental solution methods and general transient analysis. Short-duration, high-energy events such as crash, impact and bird strike are treated in the Impact, Crash & Explicit Dynamics category; explicit methods may appear here where they serve general nonlinear transient problems.
Fundamentals
Non-Linear Structural Analysis FundamentalsWhy proportional load–response assumptions break down and how non-linear analysis represents changing stiffness, geometry, material behaviour and contact.Sources of Non-linearityUnderstanding geometric, material and boundary/contact non-linearity and how several mechanisms can interact within one model.Geometric Non-linearity & Large DeformationHow structural deformation can alter geometry, stiffness and load direction sufficiently to change the response itself.Material Non-linearity & PlasticityHow yielding and plastic deformation alter stiffness, redistribute load and create permanent structural deformation.Contact Non-linearityHow interfaces that open, close, slide or separate create changing structural load paths.
Numerical Solution
Incremental Solution Methods & ConvergenceHow non-linear equilibrium is solved through load increments, iterations and convergence checks.Newton–Raphson & Non-linear EquilibriumHow iterative tangent-stiffness methods drive a non-linear structural model towards equilibrium.Load Control, Displacement Control & Arc-Length MethodsHow alternative solution controls allow unstable and post-limit structural response to be followed.Non-linear Buckling & CollapseHow imperfections, plasticity and large deformation influence realistic structural instability and collapse.
Explicit Dynamics
Implicit vs Explicit DynamicsUnderstanding the numerical and physical differences between implicit and explicit solution strategies.Explicit Dynamic Analysis FundamentalsHow explicit time integration solves severe contact, impact, large-deformation and failure problems.Time Step, Stability & Mass ScalingWhy explicit analysis requires very small stable time increments and how mass scaling must be controlled.Energy Balance & Result Verification in Explicit AnalysisUsing energy histories, momentum and numerical diagnostics to determine whether an explicit result is credible.Mesh Sensitivity, Rate Effects & Numerical RobustnessHow mesh, strain rate, failure formulation and numerical controls influence predicted transient response.
Impact & Failure
Impact AnalysisHow kinetic energy, momentum, contact duration and structural deformation interact during an impact event.Contact, Friction & Energy Transfer in ImpactHow local contact mechanics control the transfer of energy and momentum between impactor and structure.Material Failure, Damage & Element DeletionHow numerical models represent initiation, evolution and eventual loss of structural material capability.Bird-Strike AnalysisHow highly non-linear transient methods are used to represent soft-projectile impact and structural response.SPH, Lagrangian & Coupled Impact ModellingChoosing discretisation methods suited to extreme deformation in projectiles and structural targets.