1. replacement principle:
Displacement method is an analysis method based on structural elasticity principle, which solves the stress situation of the structure by considering the displacement response of the structure. It decomposes the structure into several discrete elements, assumes the form of displacement field on each element, and establishes corresponding equations by using boundary conditions and force balance conditions. By solving these equations, the displacement response and stress distribution of the structure can be obtained.
2. The definition of typical equation:
In displacement method, because of the complexity of structure and calculation, some simplified models or assumptions are often chosen to analyze the structure. The equations obtained from these models or assumptions are called typical equations, which are used to describe the response and stress of structures. Typical equations are generally derived based on specific structural forms and load conditions to satisfy mechanical equilibrium and boundary conditions.
3. According to the structural form:
The form and formalization process of a typical equation depend on the concrete structural form. For example, in the displacement analysis of beams, the corresponding typical equations can be derived according to different beam types (such as cantilever beam, simply supported beam, continuous beam, etc.). These equations are usually derived from the bending theory and stress analysis of beams.
4. According to the load:
Typical equations can also be determined according to the load conditions of the structure. For example, when analyzing a beam under uniformly distributed load, the deflection equation or bending moment equation of the beam can be derived. In the beam analysis under point load, the bearing reaction equation or shear equation of the beam can be derived. These equations can describe the displacement response and stress of the structure under different load conditions.
5. Develop further:
Displacement method is widely used in structural analysis, not only for beam and frame structures, but also for other structural forms such as plates, shells and membranes. In practical engineering, in order to solve the displacement and stress problems of complex structures, numerical methods (such as finite element method) can also be used to solve typical equations. These methods can predict the structural response more accurately and provide more comprehensive stress information.