Direct Methods for Limit and Shakedown Analysis of by Paolo Fuschi, Aurora Angela Pisano, Dieter Weichert

By Paolo Fuschi, Aurora Angela Pisano, Dieter Weichert

Articles during this ebook study a number of fabrics and the way to figure out at once the restrict nation of a constitution, within the experience of restrict research and shakedown research. except classical functions in mechanical and civil engineering contexts, the ebook stories at the rising box of fabric layout past the elastic restrict, which has additional commercial layout and technological purposes. Readers will notice that “Direct equipment” and the recommendations offered the following can in reality be used to numerically estimate the power of established fabrics equivalent to composites or nano-materials, which signify fruitful fields of destiny applications.

Leading researchers define the most recent computational instruments and optimization innovations and discover the potential of acquiring details at the restrict nation of a constitution whose post-elastic loading direction and constitutive habit will not be good outlined or popular. Readers will detect how Direct equipment permit fast and direct entry to asked details in mathematically confident manners with out bulky step by step computation.

Both researchers already or taken with the sector and useful engineers who are looking to have a landscape of contemporary tools for structural security evaluate will locate this e-book useful. It presents the reader with the most recent advancements and an important quantity of references at the topic.

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Example text

Fortunately, the quadratic variation and the discontinuities of the stress field made that only moderately sizes of the mesh were necessary in the tests, due also to efficiency of the iterative process below. 4 The Post-analysis Process After the optimization, a rigorous post-analysis is carried out: • verification of the stress vector continuity across every boundary between adjacent elements; in fact, the stress vector jump is always smaller than 10−5 ; • subdivision of each element into a large number of “subtriangles” (more than 200); accurate computation of Q1 and Q2 values, by integral calculation on each subtriangle, followed by a summation on the whole domain; • verification of the Coulomb criterion inside each subtriangle of each element; this verification is performed with the three original inequations (6), since the stress field is known at this stage.

Qid , . . ii) where the stress tensors σ are admissible, and Qd is a fixed admissible loading vector. ii) holds when all admissible fields σ can be taken into account, which is not the case in general. e. a lower bound to the exact macroscopic criterion investigated here. 32 F. Pastor et al. 2 The Mixed Kinematic Method On the other hand, a so-called mixed kinematic formulation was pioneered by Anderheggen and Knopfel [1] for finite element continuous velocity and a linearized von Mises criterion, resulting in linear programming (LP) problems.

Even in this relatively simple case of spherical voids, there is no theoretical attempt to micromechanically derive a macroscopic criterion for the Coulomb porous material. This is undoubtedly due to difficulties inherent to the Coulomb criterion which involves all the three stress invariants. Several extensions of the Gurson model taking into account void shape effects have been also proposed in order to solve various practical cases (see for example [5–7, 15, 16]). Up to our knowledge, similar theoretical studies with pressuresensitive matrices and non-spherical voids do not exist in the literature: clearly, in this case of spheroidal voids also, there is a strong need of an appropriate research effort to obtain efficient estimates.

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