What are the main challenges of nonlinear stress analysis and how do you overcome them?

2 Nonlinear geometry

Another challenge of nonlinear stress analysis is accounting for the nonlinear geometry effects that arise from large deformations, rotations, or contact interactions. These effects can significantly alter the stress distribution, stiffness, and stability of the structure, and may lead to buckling, snap-through, or post-buckling phenomena. To handle these effects, you need to use appropriate element types, mesh refinement, and solution techniques that can capture the nonlinear kinematics and equilibrium of the structure. For example, you may need to use nonlinear beam or shell elements, adaptive meshing, or arc-length methods to solve nonlinear geometry problems. Additionally, you need to check the validity of your assumptions and boundary conditions, and monitor the deformation and strain levels of the structure.

3 Nonlinear contact

Nonlinear contact is another common source of challenge in nonlinear stress analysis, as it involves the interaction between two or more bodies that may touch, separate, slide, or stick depending on the applied load and friction. Nonlinear contact can introduce discontinuities, gaps, and nonlinearities in the stiffness matrix, and may cause difficulties in finding the initial contact state, enforcing the contact constraints, and achieving convergence. To overcome these challenges, you need to define the contact pairs, contact types, contact properties, and contact algorithms carefully, and use appropriate convergence criteria, damping factors, and stabilization methods. Furthermore, you need to verify the contact status, contact pressure, and contact forces of the solution, and compare them with the expected physical behavior.

4 Nonlinear dynamics

Nonlinear dynamics is another challenging area of nonlinear stress analysis, as it deals with the transient response of the structure under dynamic loading or vibration. Nonlinear dynamics can result in complex phenomena such as resonance, damping, mode coupling, frequency shift, or chaos, which can affect the performance and safety of the structure. To perform nonlinear dynamic analysis, you need to select the appropriate time integration scheme, time step size, damping model, and loading function that can capture the nonlinear dynamic behavior of the structure. Moreover, you need to perform modal analysis, harmonic analysis, or frequency response analysis to identify the natural frequencies, mode shapes, and amplitude response of the structure, and compare them with the nonlinear dynamic solution.

5 Nonlinear optimization

Nonlinear optimization is another useful application of nonlinear stress analysis, as it allows you to find the optimal design parameters that satisfy certain objectives and constraints. For example, you may want to minimize the weight, maximize the strength, or improve the reliability of the structure under nonlinear conditions. However, nonlinear optimization can be challenging and computationally expensive, as it requires multiple nonlinear stress analyses, sensitivity analyses, and iterative algorithms to search for the optimal solution. To perform nonlinear optimization, you need to define the design variables, objective function, constraint functions, and optimization method carefully, and use efficient and robust techniques such as gradient-based methods, genetic algorithms, or surrogate models. Additionally, you need to evaluate the feasibility, optimality, and robustness of the optimal solution, and perform verification and validation.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?