These terms refer to different levels of sophistication in structural analysis, taking into account the various factors that affect the behavior of a structure under load. First-order analysis (also known as linear analysis): First-order analysis is the most basic and simplified form of structural analysis. It assumes that the structure remains linearly elastic throughout the loading process, meaning that the relationship between applied loads and resulting deformations is assumed to be linear. In this analysis, factors such as geometric nonlinearity (large deformations) and material nonlinearity (plastic behaviour) are not considered. First-order analysis is typically used for simple structures or when the expected deformations are small. The biggest advantage of using first order analysis is that the rule of superpositioning can be applied. In other words the results of multiple load cases can be superimposed in module MAXIMA. Second-order analysis (geometric nonlinear analysis): Second-order analysis incorporates nonlinear effects that are not considered in first-order analysis. It takes into account the stiffness change of an element due to the nonlinear force 'N'. Cables get more stiffness, columns less. Often called as pi-delta effect. (geometric nonlinearity, which means that the structure's behaviour is analysed considering large deformations). In this analysis, the internal forces and deformations are updated iteratively until equilibrium is reached. This allows for a more accurate representation of the structure's behaviour under applied loads, considering the effects of P-Δ (axial force-moment interaction). Second-order analysis is particularly relevant for slender structures or those subject to significant lateral loads. Third-order analysis (advanced geometric nonlinear analysis): Third-order analysis goes a step further in sophistication and considers additional factors that influence the structural behaviour. It means real equilibrium in the deformed shape. It takes into account the geometric nonlinearity that contains not only the effects of P-Δ (axial force-moment interaction), but also the P-δ (axial force-deflection interaction), allowing for the analysis of structures with more complexity. Third-order analysis is typically used for specialized cases, such as highly complex or unique structures, or cable stayed structures where accurate predictions of behaviour are crucial. Typical applications are: cable sagging, snapping through, shell buckling, membranes.
Hey could you maybe write down the commands which you used for the results? That would be very nice
Thank you for the explanation. As per you, when is it a good idea to use the third order analysis instead of 2nd order ?
YOu don't explain the differences between 1st, 2nd and 3rd order, conceptually !!!!!!!!!
These terms refer to different levels of sophistication in structural analysis, taking into account the various factors that affect the behavior of a structure under load.
First-order analysis (also known as linear analysis):
First-order analysis is the most basic and simplified form of structural analysis. It assumes that the structure remains linearly elastic throughout the loading process, meaning that the relationship between applied loads and resulting deformations is assumed to be linear. In this analysis, factors such as geometric nonlinearity (large deformations) and material nonlinearity (plastic behaviour) are not considered. First-order analysis is typically used for simple structures or when the expected deformations are small.
The biggest advantage of using first order analysis is that the rule of superpositioning can be applied. In other words the results of multiple load cases can be superimposed in module MAXIMA.
Second-order analysis (geometric nonlinear analysis):
Second-order analysis incorporates nonlinear effects that are not considered in first-order analysis. It takes into account the stiffness change of an element due to the nonlinear force 'N'. Cables get more stiffness, columns less. Often called as pi-delta effect. (geometric nonlinearity, which means that the structure's behaviour is analysed considering large deformations). In this analysis, the internal forces and deformations are updated iteratively until equilibrium is reached. This allows for a more accurate representation of the structure's behaviour under applied loads, considering the effects of P-Δ (axial force-moment interaction). Second-order analysis is particularly relevant for slender structures or those subject to significant lateral loads.
Third-order analysis (advanced geometric nonlinear analysis):
Third-order analysis goes a step further in sophistication and considers additional factors that influence the structural behaviour.
It means real equilibrium in the deformed shape.
It takes into account the geometric nonlinearity that contains not only the effects of P-Δ (axial force-moment interaction), but also the P-δ (axial force-deflection interaction), allowing for the analysis of structures with more complexity. Third-order analysis is typically used for specialized cases, such as highly complex or unique structures, or cable stayed structures where accurate predictions of behaviour are crucial.
Typical applications are: cable sagging, snapping through, shell buckling, membranes.