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Analysis according to I. order theory

Analysis according to I. order theory is the fundamental function of the program. It consists of several parts, continuously following each other. The first part is the control of inputs. It checks whether the input of necessary parts is complete and the structure meets assumptions of analysis.

The next step is the optimization (optional), which is an operation that should significantly accelerate the analysis of complex structures.

After that, composition of stiffness matrix follows. It is compiled from the partial stiffness matrices of individual members. An essential element for the analysis is a member sector. The member sector is a part of member between two joints. Each member consists of adjacent sectors lying on one straight line.

The composition of vectors on the right sides, that contain joint loads, is the next step. These values ​​contain also member loads that has been previously converted into joint loads. Number of vectors is equal to the number of load cases. The program compiles the stiffness matrix in elements.

The system of equations is solved with the help of method Sky-Line, which is effective for frame and topologically inhomogeneous structures. The advantage of this method is also the minimization of zero elements in the matrix, thereby the numerical inaccuracies is reduced.

Overall, the calculation may be time consuming when using iterative methods for dynamic and stability calculations, especially for larger structures where the numbering optimization has not been applied. As a result of the analysis, the values ​​of deformations in the joints are obtained. These values are the key data for all calculations in post processor (internal forces, reactions, member deformations, stresses).

The last part of the analysis is the preparation and saving of values ​​needed for fast results view. It means internal forces at the endpoints of members, reactions in supports and extreme values of internal forces.

Numbering optimization

Numbering optimization is a process that allows for greater speed of calculation. If optimization is enabled, the joint are renumbered in order to accelerate solving the system of equations before running the analysis. The purpose of renumbering is that the stiffness matrix have nonzero elements as much as possible centered around the main diagonal. This significantly reduces the number of operations undertaken in solving the system of equations. Renumbering is done only within the calculation, so the user's originally assigned numbering retains in the program. Optimization algorithm does not perform renumbering on structures that are divided into more separated parts.

Singularity during analysis

Singularity is the most common error that occurs during analysis. It is usually caused by insufficient support of structure or its part. It is necessary to check the supports of complete structure, as well as integrity of individual structure parts and eventually review end conditions of particular members. This error indicates that some part of the structure can move freely in space. The most often case is the member rotation about the member axis or insufficient support of planar structures in space.

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