principle of virtual work structural analysis examples

It follows that all forces explicitly appear in the equilibrium equations of the problem and the solution process involves the determination of all forces, including internal and reaction forces. While it is customary to make a distinction between externally applied loads, internal forces and reaction forces, Newton's condition for equilibrium states that the sum of all forces must vanish,without making any distinction between them. The equilibrium conditions stated by Newton's law are expressed in their most general form as vector equations, and vector algebra is required for most practical applications. Newtonian mechanics is based on the concepts of forces and moments, which are vector quantities. Consequently, work quantities are simpler to manipulate than forces and displacements, and this simplification makes work based formulations of mechanics very attractive. The mechanical work done by a force is defined as the scalar product of that force by the displacement through which it acts: work is a scalar quantity, in contrast with forces and displacements, which are vector quantities characterized by magnitudes and directions.

Dependency due to the presence of geometric uncertainty is eliminated using the M matrix approach developed earlier by Mullen and Muhanna.The concept of mechanical work is fundamental to the study of mechanics. Results are illustrated in example problems. The present work also computes an exact enclosure to the final system geometry. is utilised to obtain sharp bounds to displacements and element forces in the presence of geometric, material and load uncertainties. The mixed interval finite element formulation developed earlier by Rama Rao et al.

The present work eliminates the element force overestimation resulting in the previous formulation of Muhanna et al. Such geometric uncertainty is converted into an equivalent nodal load uncertainty. Geometric uncertainty is expressed as deviations of actual dimensions of system components from their corresponding nominal dimensions (misfitting) and is expressed in interval form. In this work, the issue of predicting structural behaviour in the presence of geometric uncertainty arising out of fabrication errors and/or thermal changes in trusses and frames is addressed.

Principle of virtual work structural analysis examples