What is Static Analysis?
10/21/2009When loads are applied to a body, the body will deform and the effect of the loads will be transmitted throughout the body. To absorb the effect of loads, the body generates internal forces and reactions at the supports to balance the applied external loads. Linear static analysis refers to the calculation of displacements, strains, and stresses under the effect of external loads based on two basic assumptions:
Static Assumption All loads are applied slowly and gradually until they reach their full magnitudes. After reaching their full magnitudes, loads will remain constant (time-invariant). This assumption allows us to disregard insignificant inertial and damping forces due to negligibly small accelerations and velocities. Time-invariant loads that induce considerable inertial and/or damping forces may warrant dynamic analysis. Dynamic loads change with time and, in many cases, induce considerable inertial and damping forces that cannot be neglected.
Linearity Assumption The relationship between loads and induced responses is linear. If you double the magnitude of loads, for example, the response of the model (displacements, strains, and stresses), will also double. You can assume that the linearity assumption is valid if:
- All the materials in the model comply with Hook’s law, that is stress is directly proportional to strain.
- The induced displacements are small enough to ignore the change in stiffness caused by loading.
- Boundary conditions do not vary during the application of loads. Loads must be constant in magnitude, direction, and distribution. They should not change while the model is deforming.
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