Damage assessment of structures with uncertainty by using mode-shape curvatures and fuzzy logic

Uncertainties associated with the structural model and measured vibration data may lead to unreliable damage detection. In this paper, we show that geometric and measurement uncertainty cause considerable problem in damage assessment which can be alleviated by using a fuzzy logic-based approach for damage detection. Curvature damage factor (CDF) of a tapered cantilever beam are used as damage indicators. Monte Carlo simulation (MCS) is used to study the changes in the damage indicator due to uncertainty in the geometric properties of the beam. Variation in these CDF measures due to randomness in structural parameter, further contaminated with measurement noise, are used for developing and testing a fuzzy logic system (FLS). Results show that the method correctly identifies both single and multiple damages in the structure. For example, the FLS detects damage with an average accuracy of about 95 percent in a beam having geometric uncertainty of 1 percent COV and measurement noise of 10 percent in single damage scenario. For multiple damage case, the FLS identifies damages in the beam with an average accuracy of about 94 percent in the presence of above mentioned uncertainties. The paper brings together the disparate areas of probabilistic analysis and fuzzy logic to address uncertainty in structural damage detection.

Polarized Ethylenes: Structures of (l,3-Dimethyl-2-imidazolidinylidene)malononitrile and (l,3-Dimethyl-2-perhydropyrimidinylidene)malononitrile

Crystal structures of the title compounds, (I) and (II), have been determined by three-dimensional diffraction methods. Crystals of CsHIoN 4 (I) are monoclinic, space group P21/a with Z = 4, Mr= 162, a = 7.965 (1), b = 16.232 (2), c = 7.343 (1) A, fl = 113.54 (1) °, V = 890.7 A 3, D,n = 1.218, D x = 1.208 gcm -3, g(Cu Ka, 2 = 1.5418/~) = 6.47 em -1, F(000) = 344. The crystals of C9H12N4 (II) are orthorhombic, space group P21en, with Z = 4, Mr = 176, a = 7.983 (3), b = 8.075 (2), c = 14.652 (3) ./k, V = 44.43/~3, Dm= 1.219, D x = 1.237 g cm -3, #(Mo Ka, ). = 0.7107 ,/k) = 0.868 cm -1, F(000) = 376. Both structures were solved by direct methods and refined to R = 5.8% for (I) and 5.3 % for (II). The C-C double-bond distances are 1.407 (3) in (I) and 1.429 (6)/~ in (II), appreciably longer than normal. The steric and push-pull effects result in rotation about the C=C bond, the rotation angles being 20.2 (3) in (I) and 31.5 (6) o in (II).

The structures of ethyl 1,2,2-tricyano-3,3-dimethylcyclopropane-1-carboxylate and ethyl 2',3,3'-tricyanocyclohexanespirocyclopropane-2'-carboxylate

The crystal and molecular structures of C ,,H,IN302 (I) and C14HIsN302 (II) have been determined by direct methods using three-dimensional X-ray diffractometer data. Crystals of (I) are orthorhombic, space group Pna21, with a = 14.662(6), b = 10.492(5), c = 7.375 (3)A, Z = 4, V = 1134.5 A 3, D O = 1.25 (by flotation), D e = 1.269 Mgm -a, g(MoKa) = 0.085 mm -1. Crystals of (II) are monoclinic, space group P21/a, with a = 7.886 (5), b = 22.011 (8), c = 8.100 (3) A, fl = 103.12 (5) °, Z = 4, V = 1369.2 A 3, D O = 1.23 (by flotation), D e = 1.255 Mg m -3, g(Mo Kct) = 0.080 mm -1. Least-squares full-matrix refinement based on 782 (I) and 1400 independent reflections (II) converged at R = 0.040 (I) and 0.042 (II). The effect of electron-withdrawing substituents on the geometry of the cyclopropane ring is discussed.

Gas-crystal photoreaction: the structures of 4,4'-dimethoxy(thiobenzophenone) (I), C15H14O2S, and 4,4'-bis(dimethylamino)thiobenzophenone (II), C17H20N2S

(I): M r = 258.34, triclinic, Pi, a = 9.810 (3), b=9.635(3), e=15.015(4)A, a=79.11(2), #= 102.38 (3), y = 107.76 (3) o, V= 1308.5 A 3, Z = 4, Din= 1.318 (3) (by flotation in KI solution), D x = 1.311 g cm -3, Cu Ka, 2 = 1.5418/~, g = 20-05 cm -1, F(000) = 544, T---- 293 K, R = 0.074 for 2663 reflections. (II): M r = 284.43, monoclinic, P2~/c, a= 17.029 (5), b=6.706 (5), c= 14.629 (4), t= 113.55 (2) ° , V=1531.4A 3, Z=4, Dm=1.230(5) (by flotation in KI solution), Dx= 1.234gem -3, Mo Ka, 2 = 0.7107 A, g = 1.63 cm-1; F(000) = 608, T= 293 K, R = 0.062 for 855 reflections. The orientation of the C=S chromophores in the crystal lattice and their reactivity in the crystalline state are discussed. The C--S bonds are much shorter than the normal bond length [1.605 (4) (I), 1.665 (8) A (II) cf. 1.71 A].

Sequence effects in structures of the dinucleotides d-pApT AND d-pTpA

The H1',H2' and H2″ regions of the 270-MHz PMR spectra of two deoxydinucleotides, d-pTpA and d-pApT, have been analyzed. The coupling constants in the sugar ring indicate that both A and T sugars have a tendency to acquire 2E conformations. There is also a marginal difference in the 2E populations of the T sugar in the two dinucleotides. The trends in the chemical shifts of base protons indicate different stacking of the bases in d-pApT and d-pTpA. The sequence effects on base stacking and pentose conformation are discussed.

Molecular structures of cytidine-5-diphosphate and cytidine-5-diphospho-choline, and their role in intermediary metabolism

The nucleotide coenzyme cytidine-5-diphospho-choline is highly folded. The CMP-5 parts of the molecules in the crystal structure are strongly linked by metal ligation and hydrogen bonds leaving the phosphoryl-choline residues relatively free. Cytidine-5-diphosphoric acid exists as a zwitterion with N31 protonated. The P−O bond lengths from the anhydride bridging oxygen in the pyrophosphate are significantly different.

A fast method of comparing protein structures

Comparative studies on protein structures form an integral part of protein crystallography. Here, a fast method of comparing protein structures is presented. Protein structures are represented as a set of secondary structural elements. The method also provides information regarding preferred packing arrangements and evolutionary dynamics of secondary structural elements. This information is not easily obtained from previous methods. In contrast to those methods, the present one can be used only for proteins with some secondary structure. The method is illustrated with globin folds, cytochromes and dehydrogenases as examples.

Volatile constituents of Clausena willdenovii: Structures of the furanoterpenes α-clausenan, diclausenan A and diclausenan B

Four furanoid terpenic compounds, α-clausenan, rosefuran (γ-clausenan) and diclausenans A and B, were isolated from the essential oil of the leaves of Clausena willdenovii. Their structures were determined by chemical and spectral data. The occurrence of a high concentration of rosefuran is noteworthy. Selenium dioxide oxidation of diclausenan gave an unusual product, identified as an epoxy-dicarbonyl compound.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

A New Type of Dihedral Angle for the Description of Bimolecular Structures

Abstract is not available.

Conformation of polypeptide-chains containing both l-residues and D-residues .2. Double-helical structures of poly-ld-peptides

Polypeptides with alternating L- and D-amino acid residues can take up stereochemically satisfactory coaxial double-helical structures, both antiparallel and parallel, which are stabilized by systematic interchain NH O hydrogen bonds. Semiempirical energy calculations over allowed regions of conformational space have yielded the characteristics of these double-helices. There are four possible types of antiparallel double-helices - A3, A4, A5 and A6, with n, the number of LD peptide units per turn, around 2.8, 3.6, 4.5 and 5.5 respectively, while for the parallel double-helices there are two types, P3 and P4, having similar helical parameters as in A3 and A4. The hydrogen-bonding scheme restricts the pitch in all the models to the narrow range of 10.0 to 11.5 Å. All these helices have large central cores whose radii increase proportionately with n. In this respect, A3 and A4 are suitable models for the structure of gramicidin A. In terms of their relative energies, antiparallel double-helices are marginally more stable than those with parallel strands. Our results indicate that the energy differences amongst the members in the antiparallel family are not significant and thus provide an explanation for the polymorphism reported for poly(γ-benzyl-LD-glutamate).

Structural studies of analgesics and their interactions. Part 4. Crystal structures of phenylbutazone and a 2 : 1 complex between phenylbutazone and piperazine

The X-ray crystal structures of 4-butyl-1,2-diphenylpyrazolidine-3,5-dione (phenylbutazone)(I). and its 2 : 1 complex (II) with piperazine have been determined by direct methods and the structures refined to R 0.096 (2 300 observed reflections measured by diffractometer) and 0.074 (2 494 observed reflections visuallyestimated). Crystals are monoclinic, space group P21/c; for (I)a= 21.695(4), b= 5.823(2), c= 27.881(4)Å, = 108.06 (10)°, Z= 8, and for (II)a= 8.048(4), b= 15.081(4), c= 15.583(7)Å, = 95.9(3)°, Z= 2. The two crystallographically independant molecules in the structure of (I) are similar except for the conformation of the butyl group, which is disordered in one of the molecules. In the pyrazolidinedione group, the two C–C bonds are single and the two C–O bonds double. The two nitrogen atoms in the five-membered ring are pyramidal with the attached phenyl groups lying on the opposite sides of the mean plane of the ring. The phenylbutazone molecule in (II) exists as a negative ion owing to deprotonation of C-4. C-4 is therefore trigonal and the orientation of the Bu group with respect to the pyrazolidinedione group is considerably different from that in (I); there is also considerable electron delocalization along the C–O and C–C bonds. These changes in geometry and electronic structure may relate to biological activity. The doubly charged cationic piperazine molecule exists in the chair form with the nitrogen atoms at the apices. The crystal structure of (II) is stabilized by ionic interactions and N–H O hydrogen bonds.

A novel amino acid racemization in vitamin b6-amino acid schiff base copper complexes: crystal structures of aquo (5'-phosphopyridoxylidene-dl-tyrosinato) copper(II) 3.5H2O and aquo (5'-phosphopyridoxylidene-dl-phenylalaninato) copper(II) 2.5H2O

A novel racemization observed in the Vitamin B6-amino acid Schiff base complexes, aquo (5'-phosphopyridoxylidene-l-tyrosinato) copper(II) and aquo (5'-phosphopyridoxylidene-l-phenylalaninato) copper(II) is described. The racemization taking place in solution under mild acidic conditions (pH 5-6) was confirmed by CD studies and the products were characterized by single crystal X-ray diffraction. The structures of both complexes show almost parallel orientation of the aromatic side chain and the pyridoxal II-system. The activation of the αCsingle bondH group due to the intermolecular II- interaction is probably the reason for the unusual racemization observed.

Metal-Nucleotide Interactions: Crystal Structures of Alkali (Li+, Na+, K+) and Alkaline Earth (Ca2+, Mg2+) Metal Complexes of Adenosine 2'-Monophosphate

Crystal structures of lithium, sodium, potassium, calcium and magnesium salts of adenosine 2'-monophosphate (2'-AMP) have been obtained at atomic resolution by X-ray crystallographic methods. 2'-AMP.Li belongs to the monoclinic space group P21 with a = 7.472(3)Å, b = 26.853(6) Å, c = 9.184(1)Å, b = 113.36(1)Å and Z= 4. 2'-AMP.Na and 2'-AMP.K crystallize in the trigonal space groups P31 and P3121 with a = 8.762(1)Å, c = 34.630(5)Å, Z= 6 and a = 8.931(4), Åc = 34.852(9)Å and Z= 6 respectively while 2'-AMP.Ca and 2'-AMP.Mg belong to space groups P6522 and P21 with cell parameters a = 9.487(2), c = 74.622(13), Z = 12 and a = 4.973(1), b = 10.023(2), c = 16.506(2), beta = 91.1(0) and Z = 2 respectively. All the structures were solved by direct methods and refined by full matrix least-squares to final R factors of 0.033, 0.028, 0.075, 0.069 and 0.030 for 2'-AMP.Li, 2'-AMP.Na, 2'- AMP.K, 2'-AMP.Ca and 2'-AMP.Mg, respectively. The neutral adenine bases in all the structures are in syn conformation stabilized by the O5'-N3 intramolecular hydrogen bond as in free acid and ammonium complex reported earlier. In striking contrast, the adenine base is in the anti geometry (cCN = -156.4(2)°) in 2'-AMP.Mg. Ribose moieties adopt C2'-endo puckering in 2'-AMP.Li and 2'-AMP.Ca, C2'-endo-C3'-exo twist puckering in 2'-AMP.Na and 2'-AMP.K and a C3'-endo-C2'-exo twist puckering in 2'-AMP.Mg structure. The conformation about the exocyclic C4'-C5' bond is the commonly observed gauche-gauche (g+) in all the structures except the gauche- trans (g-) conformation observed in 2'-AMP.Mg structure. Lithium ions coordinate with water, ribose and phosphate oxygens at distances 1.88 to 1.99Å. Na+ ions and K+ ions interact with phosphate and ribose oxygens directly and with N7 indirectly through a water oxygen. A distinct feature of 2'-AMP.Na and 2'-AMP.K structures is the involvement of ribose O4' in metal coordination. The calcium ion situated on a two-fold axis coordinates directly with three oxygens OW1, OW2 and O2 and their symmetry mates at distances 2.18 to 2.42Å forming an octahedron. A classic example of an exception to the existence of the O5'-N3 intramolecular hydorgen bond is the 2'-AMP.Mg strucure. Magnesium ion forms an octahedral coordination with three water and three phosphate oxygens at distances ranging from 2.02 to 2.11Å. A noteworthy feature of its coordination is the indirect link with N3 through OW3 oxygen resulting in macrochelation between the base and the phosphate group. Greater affnity of metal clays towards 5' compared to 2' and 3' nucleotides (J. Lawless, E. Edelson, and L. Manring, Am. Chem. Soc. Northwest Region Meeting, Seattle. 1978) due to macrochelation infered from solution studies (S. S. Massoud, H. Sigel, Eur. J. Biochem. 179, 451-458 (1989)) and interligand hydrogen bonding induced by metals postulated from metal-nucleotide structures in solid state (V. Swaminathan and M. Sundaralingam, CRC. Crit. Rev. Biochem. 6, 245-336 (1979)) are borne out by our structures also. The stacking patterns of adenine bases of both 2'-AMP.Na and 2'-AMP.K structures resemble the 2'-AMP.NH4 structure reported in the previous article. 2'-AMP.Li, 2'-AMP.Ca and 2'-AMP.Mg structures display base-ribose O4' stacking. An overview of interaction of monovalent and divalent cations with 2' and 5'-nucleotides has been presented.

Crystal structures and thermal analyses of alkyl 2-deoxy-alpha-D-arabino-hexopyranosides

The crystal structures of alkyl 2-deoxy-alpha-D-arabino-hexopyranosides, with the alkyl chain lengths from C-8 to C-18, are established by the single crystal X-ray structural determination. The even-alkyl chain length derivatives crystallized orthorhombic, with space group P2(1)2(1)2(1), whereas the odd-alkyl chain length derivatives crystallized monoclinic, with space group P2(1). The sugar moieties retained a C-4(1) chair conformation and the conformation of the alkyl chains was all-trans. The molecules formed a bilayer structure, in which alkyl chains were interdigitated.The hydrogen bonds, originating from the sugar moieties, were observed in adjacent layers and also within the same layer, resulting in the formation of infinite chains. The alkyl chains arranged parallel to each other and formed planar structures. The thermal properties of the alkyl 2-deoxy glucosides were analyzed further. It was observed that none of the derivatives exhibited mesomorphism. This study establishes that the absence of the hydroxyl group at C-2 of the sugar moiety results in a non-mesogenic nature of the alkyl 2-deoxy-alpha-D-glycosides, as opposed to the profound mesogenic nature of the normal alkyl glycosides.