The most widely used method for simulating the non-linear behaviour of concrete and masonry structures is the Newton–Raphson method with arc-length control (N-R method). However, this method may fail to produce converged results because of softening, negative tangent stiffness, bifurcations or snap-back. Sometimes, convergence can be obtained by controlling degrees of freedom in the failure process zone or by applying sequentially linear analysis (SLA). However, the location of the failure is often not known a priori and geometrical non-linearity needs to be included. Recently, incremental sequentially linear analysis (ISLA) has been proposed, which is based on a combination of the N-R method and SLA. The solution search path follows damage cycles sequentially with secant stiffness corresponding to local damage increments, which traces both damage history (explicit) and displacement history (implicit). The objective of this paper is to demonstrate that ISLA can be applied to problems that behave geometrically nonlinear in addition to physically nonlinear. In this paper, we introduce a method that combines ISLA with indirect displacement control. This method stabilises localised damage process areas and avoids the global unloading caused by geometrical and physical non-linearity. The method uses one or more control points, which are positioned independently of the failure process zones. Two masonry walls were tested and analysed. The load was perpendicular to their planes and evenly distributed. The walls were supported on two or four edges. Stable post-peak results were computed for large geometrical non-linear displacements, and localised crack propagation was computed robustly and correctly.

In the past decades, great progress has been made in analyzing lateral torsional buckling of slender beams. The phenomena has been accurately described by differential equations, closed form solutions are available for specific cases and the solution for any load and any boundary condition can be obtained by finite element analysis. Timber and steel design standards provide a procedure based on equivalent moment factors. With this procedure, beams can be designed straightforwardly. However, modern designers continue to push the envelope and more irregular load patterns are found, on which the design standards do not provide solutions. Consequently, designers are forced to determine the equivalent moment factors based on case-specific literature and/or conservative assumptions. Unfortunately, this makes many challenging modern designs uneconomical. Furthermore, significant inconsistencies between the different design procedures are found. For that purpose, this paper proposes a solution in the form of a general formulation to determine equivalent moment factors for any loading on a single-span beam for both free and restrained lateral bending and/or warping at the supports, for both I-sections and rectangular slender sections loaded in the shear center. It is shown that the obtained moment factors are accurate and in good agreement with design standards and literature, and a wide range of irregular load patterns is considered.

The problem minimizing the number of specimens required for fatigue data analysis is considered in this research. Assuming unknown hyperparameters described via prior distributions, a hierarchical Bayesian model with accumulated prior information was proposed to deal with this issue. One of the main advantages of hierarchical Bayesian model over the empirical Bayesian model is that the prior distributions with hierarchical structure can incorporate structural prior and subjective prior simultaneously. The probabilistic stress-cycle (P-S-N) curves are generated from the predictive distributions, involving both the randomness of parameters and the scatter of observations, and calculated by an identical hierarchical structure. The numerical calculation is done via the Gibbs sampler, which makes the whole process simple and intuitive.