Download Numerical methods in structural mechanics by Zdeněk Bittnar; Jiří Šejnoha PDF

By Zdeněk Bittnar; Jiří Šejnoha

This publication presents a transparent figuring out of the character and theoretical foundation of the main customary numerical equipment - the finite point strategy (FEM) and the boundary aspect technique (BEM) - whereas while proposing the main promising instructions for destiny advancements. recognition is paid mostly to these tools that experience confirmed to be the main trustworthy and effective, in addition to these tools at present less than swift improvement. Examples have been chosen both to demonstrate quite a few computational algorithms and evaluate their accuracy and efficacy or to explain the mechanical tactics lower than research, whereas conventional examples which are already coated by means of typical textbooks were intentionally passed over. Emphasis is put on the knowledge of uncomplicated ideas, instead of at the info of person numerical algorithms. The publication covers all subject matters crucial for college students of undemanding and intermediate classes on numerical equipment in sturdy mechanics, and it additionally serves as an invaluable reference for researchers and different execs. This booklet used to be lately translated from the very hot, unique Czech variation

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204). 7) into the variational principle, we arrive at the functional 50 CHAPTER 1. BASIC NOTIONS, EQUATIONS AND PRINCIPLES In addition to the displacements u^ and u^\ also the multipliers A = n^W1) = —n( 2 )

A number of elements violating the continuity condition have been proposed, especially for the solution of plates and shells. At any rate, the element must always satisfy the condition of completeness. If the approximation functions are continuous but not complete, the solution converges (sometimes even monotonically) to a wrong result. For nonconforming elements satisfying the condition of completeness but not that of continuity, it is necessary to check that the condition of completeness is satisfied by an assembly of elements.

126]). The structure of an FEM model is closely related to the corresponding variational principle. Modern BEM techniques (symmetric formulations) are also derived from suitable variational principles. 1 Principle of virtual work (PVW) The PVW has two basic versions: • the principle of virtual displacements (PVD), and • the principle of virtual forces (PVF). The principle of virtual displacements is usually written as The left-hand side represents the virtual work of internal forces (stresses) while the righthand side corresponds to the virtual work of external forces.

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