By Zdeněk Bittnar; Jiří Šejnoha
This booklet presents a transparent knowing of the character and theoretical foundation of the main wide-spread numerical tools - the finite aspect approach (FEM) and the boundary aspect technique (BEM) - whereas while providing the main promising instructions for destiny advancements. consciousness is paid generally to these tools that experience confirmed to be the main trustworthy and effective, in addition to these equipment at the moment lower than speedy improvement. Examples have been chosen both to demonstrate numerous computational algorithms and evaluate their accuracy and efficacy or to clarify the mechanical strategies less than research, whereas conventional examples which are already lined by way of usual textbooks were intentionally passed over. Emphasis is put on the knowledge of uncomplicated rules, instead of at the information of person numerical algorithms. The publication covers all issues crucial for college students of hassle-free and intermediate classes on numerical equipment in sturdy mechanics, and it additionally serves as an invaluable reference for researchers and different execs. This ebook was once lately translated from the very hot, unique Czech variation
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Extra resources for Numerical methods in structural mechanics
106), we see that the occurrence of material instability is indicated by the loss of positive definiteness of the material stiffness matrix D: This condition coincides with the singularity of the symmetric part of £>, For a symmetric tangent stiffness matrix D = DT, the loss of material stability coincides with the limit point where dcr = Ddcr = 0 and with the loss of uniqueness. 66). In the post-peak regime the "hardening" modulus becomes nonpositive, (-E) < H < 0. 4. 108) we get the stability condition It can be shown that for associated plasticity (/ = g) the loss of material stability is possible when the hardening modulus H is zero or negative.
This means that the algorithm derived from the Castigliano principle corresponds to the force method. 7 Convergence criteria The FEM replaces the continuous idealized structure by a system of elements. accuracy of the solution depends on The • the parameters of the mesh (number of elements and approximation of the boundary), and • the type of approximation of the unknown functions across the element. An accurate solution can be obtained only if the approximation functions satisfy the convergence criteria expressed by the conditions of • continuity and • completeness.
Four enhanced continuum approaches limiting the width of localization zone have so far proved to be successful: 1. Nonlocal continuum. Nonlocal (integral) localization limiters replace some quantities by their weighted averages taken over a certain neighborhood of the material point under consideration. Differential localization limiters add terms with higher-order derivatives of strain (or stress) into the constitutive equations. 2. Gradient-dependent softening plasticity theory. 3. Cosserat (micropolar) continuum.