3.6.1: Analyze

With geometry, supports and loads defined, the structural model is ready for processing. The “Analyze”-component computes the mechanical response for each load case and adds this information to the model.

The algorithm behind the “Analyze”-component neglects the change of length in axial or in-plane direction which accompanies lateral deformations. This is justified in case of displacements which are small with respect to the dimensions of a beam of shell. For dealing with situations where this condition does not hold, geometric non-linear calculations need to be used (see sections 3.5.3 and 3.5.4).

Fig. 3.6.1: Deflection of simply supported beam under single load in mid-span and axial, compressive load.

Fig. 3.6.1 shows the definition of a beam with two load-cases "LCA" and "LCB". A transverse load in mid-span acts in both load-cases. "LCA" features an additional axial compression load of 60kN, "LC_B" a tensile axial load of same size. In the absence of additional definitions with regards to the calculation types of the load-cases via a "Load-Case-Combination Options"-component the "Analyze"-component performs by default a first order theory calculation. This results in the same maximum displacement of 17.7cm for both load-cases.

The "Analyze"-component outputs not only the maximum nodal displacement (in centimeter) but also the maximum resultant force of the calculated load-cases (in kilo Newton) and the structure's internal deformation energy - section 3.6.2 contains details on work and energy. These values can be used to rank structures in the course of a structural optimization procedure: the more efficient a structure, the smaller the maximum deflection, the amount of material used and the value of the internal elastic energy. Real structures are designed in such a way that their deflection does not impair their usability. See section A.2.3 for further details. Maximum deflection and elastic energy both provide a benchmark for structural stiffness, yet from different points of view: The value of elastic energy allows to judge a structure as a whole; The maximum displacement returns a local peak value.

The "LoadCases"-input lets one select the load-case-combinations and load-cases to be considered in the analysis. By default all load-cases get computed.

Fig. 3.6.3 shows the same basic system as before. This time a "Load Case Combination"-component sets the load-cases analysis type to second order theory (Th. II). At the component's "LCase"-input the simplified regular expression "LC$" selects all load-cases with names starting with "LC". Setting "CombiNII" to false lets the "Analyze"-component compute the $N^{II}$for each load-case individually. The second order normal forces $N^{II}$soften the system when compressive, stiffen it when tensile. Therefore the maximum displacements and elastic energies of "LCA" and "LCB" differ.

Setting "NoTenNII" of the "Load Case Combination"-component to "true" would have resulted for "LC_B" in the same maximum displacement as in the example above since this options disregards the stiffening effect of normal forces.

For "CombiNII" equal to true the minimum normal force of both load-cases (N = -60kN) would have been used as $N^{II}$. Thus both load-cases "LCA" and "LCB" would have rendered a maximum displacement of 26.7cm.

Fig. 3.6.3: Deflection of simply supported beam under single load in mid-span and axial, compressive load based on second order theory small displacement calculation.

In order to view the deflected model use the “ModelView”-component (see section 3.6.1) and select the desired load-case using the "Load Case Selector"-component.

Looking at fig. 3.6.2 and fig. 3.6.3 one notices that only beam center axes are shown. In order to see beams or shells in a rendered view, add a “BeamView”- or “ShellView”-component after the “ModelView”. See sections 3.6.7 and 3.6.11 for details.