Topology Optimization for Nonlinear Material Structures Based on Proportional Technique

芝浦工業大学32169甲第248

Dimension reduction for elastoplastic rods and homogenization of elastoplastic lattices

We derive effective equations for periodic lattices of linearly elastoplastic rods in the limit of both infinitesimal periodicity and infinitesimal relative width of the rods. For this derivation we use the method of evolutionary Γ-convergence for quadratic rate-independent systems. As a first step towards this goal we derive effective equations for a single rod. After introducing appropriate scalings, the main difficulty lies in the proof of Γ-convergence for the stored energy. For the study of periodic lattices we then introduce the notion of periodic graph frameworks, discuss infinitesimal rigidity properties of such frameworks and define a notion of two-scale convergence. The stored energy of a lattice of rods ist just the sum of the energies of the individual rods, coupled by boundary conditions at the nodes. For this energy we again prove Γ-convergence. In the presence of volume loads we observe qualitatively different behaviour depending on the relative rate of convergence of the periodicity parameter and the thickness parameter

3-D inelastic analysis methods for hot section components (base program)

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described

Numerical Verification Method of Solutions for Elliptic Variational Inequalities

In this chapter, we propose numerical techniques which enable us to verify the existence of solutions for the free boundary problems governed by two kinds of elliptic variational inequalities. Based upon the finite element approximations and explicit a priori error estimates for some elliptic variational inequalities, we present effective verification procedures that, through numerical computation, generat a set which includes exact solutions. We describe a survey of the previous works as well as show newly obtained results up to now

Research in structural and solid mechanics, 1982

Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed

On the Equivalence between the Additive Hypo-Elasto-Plasticity and Multiplicative Hyper-Elasto-Plasticity Models and Adaptive Propagation of Discontinuities

Ductile and brittle failure of solids are closely related to their plastic and fracture behavior, respectively. The two most common energy dissipation mechanisms in solids possess distinct kinematic characteristics, i.e. large strain and discontinuous displacement, both of which pose challenges to reliable, efficient numerical simulation of material failure in engineering structures. This dissertation addresses the reliability and efficiency issues associated with the kinematic characteristics of plasticity and fracture. At first, studies are conducted to understand the relation between two well recognized large strain plasticity models that enjoy widespread popularity in numerical simulation of plastic behavior of solids. These two models, termed the additive hypo-elasto-plasticity and multiplicative hyper-elasto-plasticity models, respectively, are regarded as two distinct strategies for extending the classical infinitesimal deformation plasticity theory into the large strain regime. One of the most recent variants of the additive models, which features the logarithmic stress rate, is shown to give rise to nonphysical energy dissipation during elastic unloading. A simple modification to the logarithmic stress rate is accordingly made to resolve such a physical inconsistency. This results in the additive hypo-elasto-plasticity models based on the kinetic logarithmic stress rate in which energy dissipation-free elastic response is produced whenever plastic flow is absent. It is then proved that for isotropic materials the multiplicative hyper-elasto-plasticity models coincide with the additive ones if a newly discovered objective stress rate is adopted. Such an objective stress rate, termed the modified kinetic logarithmic rate, reduces to the kinetic logarithmic rate in the absence of strain-induced anisotropy which is characterized as kinematic hardening in the present dissertation. In the second part of the dissertation, the computational complexity of finite element analysis of the onset and propagation of interface cracks in layered materials is addressed. The study is conducted in the context of laminated composites in which interface fracture (delamination) is a dominant failure mode. In order to eliminate the complexities of remeshing for constant initiation and propagation of delamination, two hierarchical approaches, the extended finite element method (XFEM) and the s-version of the finite element method (s-method) are studied in terms of their effectiveness in representing displacement discontinuity across delaminated interfaces. With one single layer of 20-node serendipity solid elements resolving delamination-free response of the layered materials, it is proved that the delamination representations based on the s-method and the XFEM result in the same discretization space as the conventional non-hierarchical ply-by-ply approach which employs one layer of solid elements for each ply as well as double nodes on delaminated interfaces. Delamination indicators based on the s-method representation of delamination are then proposed to detect the onset and propagation of delamination. An adaptive methodology is accordingly developed in which the s-method displacement field enrichment for delamination is adaptively added to interface areas with high likelihood of delamination. Numerical examples show that the computational cost of the adaptive s-method is significantly lower than that incurred by the conventional ply-by-ply approach despite the fact that the two approaches produce practically identical results

A novel positive/negative projection in energy norm for the damage modeling of quasi-brittle solids

The asymmetric tensile/compressive material behavior and microcracks closure-reopening (MCR) effects exhibited by quasi-brittle solids are of significant importance to the nonlinear responses of engineering structures under cyclic loading, e.g., earthquake excitations. Based on our previous work (Cervera et al., 1995; Faria et al., 1998; Wu et al., 2006) this work addresses a novel thermodynamically consistent unilateral damage model for concrete. In particular, the positive/negative projection (PNP) of the effective stress tensor and the additive bi-scalar damage constitutive relation are maintained owing to the conceptual simplicity and computational efficiency. It is found that the classical PNP widely adopted in the literature is not optimal for this damage model, since the resulting stiffness is not always of major symmetry. Consequently, a well-defined free energy potential does not exist in general cases and the model cannot be cast into the framework of thermodynamics with internal variables. Furthermore, the damage induced anisotropy cannot be captured, exhibiting excessive lateral deformations under uniaxial tension. To overcome the above issues, a novel PNP, variationally interpreted as the closest point projection of the effective stress in energy norm, is proposed with closed-form solution. With the novel PNP, the secant stiffness tensor of the proposed unilateral damage model always possesses major symmetry and exhibits orthotropic behavior under uniaxial tension and mixed tension/compression. The corresponding thermodynamics framework is then given, resulting in an energy release rate based rounded-Rankine type damage criterion appropriate for tensile failure in quasi-brittle solids. Several numerical examples of single-point verifications and benchmark tests are presented. It is demonstrated that the proposed model is capable of characterizing localized failure of concrete under proportional and non-proportional static loading, as well as the MCR effects under seismic cyclic loading.Peer ReviewedPostprint (author's final draft

Simulation Modeling

The book presents some recent specialized works of a theoretical and practical nature in the field of simulation modeling, which is being addressed to a large number of specialists, mathematicians, doctors, engineers, economists, professors, and students. The book comprises 11 chapters that promote modern mathematical algorithms and simulation modeling techniques, in practical applications, in the following thematic areas: mathematics, biomedicine, systems of systems, materials science and engineering, energy systems, and economics. This project presents scientific papers and applications that emphasize the capabilities of simulation modeling methods, helping readers to understand the phenomena that take place in the real world, the conditions of their development, and their effects, at a high scientific and technical level. The authors have published work examples and case studies that resulted from their researches in the field. The readers get new solutions and answers to questions related to the emerging applications of simulation modeling and their advantages