10 Chapter 9Figure 9.1. Classic bit and qubit represented by two electronic levels in a sphe...Figure 9.2. A typical checkerboard pattern of a continuum structureFigure 9.3. Polar plot of the quantum gate for a qubitFigure 9.4. Finite element encoding scheme and topological formFigure 9.5. Flowchart for the presented quantum-inspired methodologyFigure 9.6. Schematic indication of the advantage of quantum annealing over clas...Figure 9.7. The diagram of element density updatingFigure 9.8. Design domain of a short cantileverFigure 9.9. Result of different initial distribution of material schemesFigure 9.10. Result of different methodsFigure 9.11. A wing rib structure under multiple loadsFigure 9.12. Topological configuration of wing rib under different methods
11 Chapter 10Figure 10.1. Quarter-car model rolling at constant speed on an uneven road with ...Figure 10.2. Amplitude ratio (red) and rms ratio (blue) for two damping values a...Figure 10.3. Half-car model rolling on a random road profile with two degrees of...Figure 10.4. Root mean square ratios of the response and excitation of the half-...Figure 10.5. Resonance and absorption speeds for k=1,2,3,… calculated from equat...Figure 10.6. Extended half-car model with four degrees of freedom and two viscoe...Figure 10.7. Related rms ratios of all displacements versus the speed frequency ...Figure 10.8. Mean amplitudes and densities of the displacements At and Bt versus...Figure 10.9. Resonance of the resultant mean amplitude for growing noise that in...Figure 10.10. Resonance reduction of the mean amplitude Vm for growing noise int...Figure 10.11. Resonance induction from blue to red resonance peaks for growing n...Figure 10.12. Limit cycles and transient projections of angles Δτ, Ψt and their ...Figure 10.13. Boundaries for almost sure stability and stability in mean. Critic...
12 Chapter 11Figure 11.1. Cumulative distribution function and robustness level. For a color ...Figure 11.2. Deign acceleration response spectra for damping factors 0.02, 0.05 ...Figure 11.3. Building modelFigure 11.4. Acceleration response spectra of seismic motions at bedrock and sur...Figure 11.5. Histogram of observed maximum inter-story drift anglesFigure 11.6. Observed maximum inter-story drift angles of each storyFigure 11.7. A 20-story shear frame model (Ohsaki et al. 2019)Figure 11.8. Relation between the maximum inter-story drift and order k for the ...Figure 11.9. Distributions of additional damping coefficients: (a) Pareto optima...
List of Tables
1 Chapter 2Table 2.1. Some parametric classes of correlation functions for a Gaussian proce...Table 2.2. COV values of the stochastic displacement statically determinate stoc...Table 2.3. Example 1: COV values of the redundant force X for L = 10 and for L =...Table 2.4. Example 1: COV values of the redundant force X for L = 10 and for L =...
2 Chapter 3Table 3.1. Mean values and standard deviations of the buckling load of the von M...Table 3.2. Results of optimizations of the three-bar truss example with random c...Table 3.3. Results of optimizations of the three-bar truss example with random h...Table 3.4. Mean value and standard deviation of the compliance of the design obt...Table 3.5. Results of the cantilever beam example with random Young’s modulus
3 Chapter 4Table 4.1. Knowledge entity of the variable representationTable 4.2. Definition of a variable knowledge entity
4 Chapter 5Table 5.1. Reliability and engineering confidence matrix
5 Chapter 7Table 7.1. Bounds of the vertical displacements at nodes 3, 4, 5 and 6 of the te...Table 7.2. Physical parameters of the plane frame (m)Table 7.3. Bounds of the horizontal displacements at nodes 188, 192, 198 and 202...
6 Chapter 8Table 8.1. Deflection bounds (in m) and “error in bound” εb % evaluated at x = 2...
7 Chapter 9Table 9.1. The number of iterations and final compliance of different methods
8 Chapter 11Table 11.1. Sample size requirements for α = γ = 0.9Table 11.2. Content ratio for order statistics of α = 0.9, n = 150Table 11.3. Optimal solutions (cross-sectional areas of braces, unit: 102 mm2)Table 11.4. Summary of observed maximum inter-story drift anglesTable 11.5. Summary of observed maximum inter-story drifts
Guide
1 Cover
5 Preface: Short Bibliographical Presentation of Prof. Isaac Elishakoff
8 Index
11 Other titles from ISTE in Mechanical Engineering and Solid Mechanics
Pages
1 v
2 iii
3 iv
4 xi
5 xii
6 xiii
7 xiv
8 xv
9 xvi
10 xvii
11 xviii
12 xix
13 xx
14 xxi
15 xxii
16 xxiii
17 xxiv
18 xxv