By Zdeněk Bittnar; Jiří Šejnoha
This publication presents a transparent realizing of the character and theoretical foundation of the main regular numerical equipment - the finite point technique (FEM) and the boundary point approach (BEM) - whereas while proposing the main promising instructions for destiny advancements. cognizance is paid usually to these equipment that experience confirmed to be the main trustworthy and effective, in addition to these tools presently lower than speedy improvement. Examples have been chosen both to demonstrate a number of computational algorithms and examine their accuracy and efficacy or to explain the mechanical methods lower than research, whereas conventional examples which are already lined through regular textbooks were intentionally passed over. Emphasis is put on the certainty of uncomplicated ideas, instead of at the info of person numerical algorithms. The e-book covers all themes crucial for college students of effortless and intermediate classes on numerical tools in good mechanics, and it additionally serves as an invaluable reference for researchers and different pros. This publication used to be lately translated from the very hot, unique Czech version
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Extra info for Numerical methods in structural mechanics
From the numerical point of view, local models are characterized by spurious sensitivity of the results to the mesh size. Moreover, the shape of the mesh causes certain directions (along the element sides or diagonals) to be preferred as directions of localization bands. 1 Model of brittle damage Constitutive equations of damage mechanics make use of appropriate state functions. 10. For the present purpose, we have to introduce only the free energy density, which is in damage mechanics denoted by p&.
2 45 45 Variational principles Variational principles directly follow from the PVW: • The principle of virtual displacements (PVD) leads to the Lagrange variational principle. • The principle of virtual forces (PVF) leads to the Castigliano variational principle. The Lagrange principle can be formulated as the principle of minimum potential energy: Among all kinematically admissible states of an elastic body, the actual state minimizes the total potential energy, where is the strain energy, and is the energy of external forces (external work).
Finally, it can be proved that the stationary value II* of the functional Ur is equal to the actual potential energy stored in the anisotropic and heterogeneous body, where (Fig. 26: A potential energy density and is the vector of eigenstrains. The functional II attains its maximum (82U < 0) if [D] is positive definite and its minimum if [D] is negative definite. 2 Dual variational principle for body with prescribed surface tractions In this section we augment the dual Hashin-Shtrikman variational principle for a body with prescribed surface tractions p by introducing eigenstrains p, into the formulation.
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