The application of gradient-based methods to structural optimization problems usually requires the determination of displacement sensitivities with respect to design variables. In this regard, it is important to have at hand comprehensive methods for sensitivity analysis, which show stability, efficiency and accuracy. Particularly, application of the semi-analytical method for linear and non-linear problems is generally a good trade-off between formulation simplicity and accuracy. In spite of that, semi-analytical methods are known to behave pathologically for shape design variables when the structure is subjected to rigid rotations. A large number of solutions for this problem have been presented in last years, although the formulation involved is generally not trivial, especially in the nonlinear case. A recent method, which adopts the semi-analytical approach and uses complex variables has rendered very promising results for all the aforementioned aspects: stability, efficiency and accuracy. Additionally, it is simple to codify. The present contribution is concerned with the application of this sensitivity analysis method to geometrically nonlinear truss problems. To this end, a finite element formulation is presented and displacement sensitivities are evaluated with respect to material and shape design variables. The results are compared to those obtained using the semi-analytical method with real variables and to global finite differences. An example demonstrates the potentiality of this new approach.

The pursuit to reduce manufacturing costs and increase product quality has led industries to use commercial codes and appropriate material models to simulate a wide range of metal forming operations. This scenario has prompted a healthy discussion on the strategies to obtaining constitutive parameters able to yield accurate numerical predictions. Optimization‐based parameter identification techniques have opened completely new routes to determine material parameters for this class of forming problems. Notwithstanding, the most appropriate optimization strategy (or development of new ones) for the trinomial forming operation – constitutive model – constitutive parameters is still open to debate. This work highlights the important role that optimization strategies play to determine parameters of constitutive models. A brief description of gradient‐based, gradient‐free and hybrid optimization approaches is presented within the framework of parameter identification. Comparative studies and applications to classical and damaged material models are also discussed.

Purpose – Parameter identification is a technique which aims at determining material or other process parameters based on a combination of experimental and numerical techniques. In recent years, heuristic approaches, such as genetic algorithms (GAs), have been proposed as possible alternatives to classical identification procedures. The present work shows that particle swarm optimization (PSO), as an example of such methods, is also appropriate to identification of inelastic parameters. The paper aims to discuss these issues. Design/methodology/approach – PSO is a class of swarm intelligence algorithms which attempts to reproduce the social behaviour of a generic population. In parameter identification, each individual particle is associated to hyper-coordinates in the search space, corresponding to a set of material parameters, upon which velocity operators with random components are applied, leading the particles to cluster together at convergence. Findings – PSO has proved to be a viable alternative to identification of inelastic parameters owing to its robustness (achieving the global minimum with high tolerance for variations of the population size and control parameters), and, contrasting to GAs, higher convergence rate and small number of control variables. Originality/value – PSO has been mostly applied to electrical and industrial engineering. This paper extends the field of application of the method to identification of inelastic material parameters.

Parameter identification is a technique which aims at determining model parameters based on a combination of experimental and numerical procedures. This work addresses identification of material parameters for elastic-plastic problems using optimization methods. Firstly, a comparative study is presented in which optimization techniques based on Genetic Algorithms, Univariate, Steepest Descent and BFGS methods are discussed. Identification of Carbon steel parameters based on tensile tests illustrates application of the BFGS, GA and GA-BFGS hybrid methods.

This paper discusses some thermodynamic aspects in association with a large strain/large displacement elastic-plastic formulation aiming at application to metal forming problems. The mechanical solution adopts the multiplicative decomposition of the gradient of deformation into elastic, plastic and thermal components. The approach is illustrated by analysing the thermal effects in the plastic deformation of low-carbon steel specimens subject to tensile loading.