Dept. of Theoretical and Applied Mechanics (1926-2006)
http://hdl.handle.net/2142/178
Sat, 07 Mar 2015 01:43:22 GMT2015-03-07T01:43:22ZAn Investigation of the Multiple Scattering of Waves in Two-Dimensional Random Media
http://hdl.handle.net/2142/72620
An Investigation of the Multiple Scattering of Waves in Two-Dimensional Random Media
Numerical studies of the ensemble average, or coherent, wave in a two-dimensional random medium have been undertaken for the steady-state and transient cases. The medium consisted of a tensioned mesh with a uniform distribution of point masses attached at the intersection points of the mesh. For the steady-state case, a random distribution of springs was also added to the mesh points. Scatterer density and scatterer strength were varied by changing the number of added springs and their stiffness, respectively. The average center deflection for several hundred mesh configurations of a given scatterer density and strength were compared with the predictions of the quasicrystalline approximation (QCA) and coherent potential approximation (CPA) theories. For the transient case, a random distribution of additional point masses was added to act as the scatterers. The mesh was subjected to an impulse force at one end, and the measured phase speed and attenuation were again compared with the predictions of the QCA and CPA theories. In addition, spatial-averaged results were compared with ensemble-averaged results for the transient mesh. In both the steady-state and transient cases, the comparisons indicate that neither theory holds a distinct advantage over the other in terms of accuracy, and both may appear valid to the experimentalist in the lab or field. Finally, the use of multiple scattering theory to predict the modal density of a random medium was demonstrated for a thin plate with circular holes.
Applied Mechanics; Physics, Acoustics
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/2142/726201993-01-01T00:00:00ZCalculation of Notch Strains Under Multiaxial Nominal Loading
http://hdl.handle.net/2142/72621
Calculation of Notch Strains Under Multiaxial Nominal Loading
An approximate analytical method is developed to calculate strains at stress concentrators in structures of elastic-plastic, isotropic material subjected to proportional and nonproportional multiaxial nominal loading. The method uses anisotropic plasticity theory to define a structural yield surface in nominal stress space that incorporates both the isotopic material properties and the anisotropic geometry factors of the notch, and accounts for varying degrees of constrained plastic flow at the stress concentrator. Plastic strain increments at the stress concentrator and anisotropic work-hardening effects are then related to this yield surface using standard methods of plasticity.; The method is applied to mildly and sharply notched shafts, and a plate with a central through hole subjected to proportional and nonproportional nominal loading. The results of these calculations are compared with experimental results of a mildly notched shaft subjected to combined tensile and torsional load, and with extensive finite element analyses of all of the structures.; The strain calculations agree well with both qualitatively and quantitatively with the experiments and finite element calculations when using an appropriate uniaxial load-notch plastic strain relationship, and are suitable for strain-life fatigue calculations.
Applied Mechanics; Engineering, Mechanical
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/2142/726211993-01-01T00:00:00ZNumerical and Laboratory Studies of Ultrasonic Anderson Localization
http://hdl.handle.net/2142/72619
Numerical and Laboratory Studies of Ultrasonic Anderson Localization
A numerical study of Anderson localization in two dimensions and a laboratory study of weak localization in three dimensions are presented. The two-dimensional study was performed by mathematically modelling a system of masses connected to a rigid base by springs of random stiffness. The masses were connected together by inextensible, massless strings. The resulting system of equations was then solved on a digital computer by stepping forward in time and solving explicitly for the displacements at each time step. Plots of the second moment of energy vs. time were made for different amounts of disorder, with values for the ratio of randomness to coupling strength (W/V) ranging from 6.0 to 9.0. No mobility edge was found, indicating that all modes were exponentially localized regardless of the degree of disorder. The three-dimensional study was performed by scattering a beam of 7 MHz ultrasound at a cell containing a slurry of glass or PMMA spherical beads and water, and measuring the backscattered energy as a function of angle. In accord with theoretical predictions, an enhanced backscatter peak with a width of 12 degrees and a magnitude twice that of the large-angle scattered energy was observed with the glass beads in a water slurry. An ultrasonic beam splitter was designed and successfully implemented to observe the small-angle scattered energy.
Applied Mechanics; Physics, Acoustics
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/2142/726191992-01-01T00:00:00ZBasic Studies in Nonlinear Photomechanics
http://hdl.handle.net/2142/72618
Basic Studies in Nonlinear Photomechanics
Applied Mechanics
Sat, 01 Jan 1977 00:00:00 GMThttp://hdl.handle.net/2142/726181977-01-01T00:00:00ZNumerical Analysis of a Generalized Plane Plastica
http://hdl.handle.net/2142/71698
Numerical Analysis of a Generalized Plane Plastica
A numerical procedure is developed for finding the displacements, internal forces, and reaction forces on any planar, continuous, and flexible structural member such as a beam, column, ring, or simply-connected frame. Euler-Bernoulli theory, in which plane sections remain plane and strains are small, is assumed. Large displacements and rotations; linear elastic, nonlinear elastic and elastic-plastic material behavior; and general cross section shapes are admitted. For nonlinear elastic analysis a multi-linear stress-strain law is used, thereby allowing an accurate approximation to the constitutive laws of actual materials. For elastic-plastic analysis a more specific tri-linear stress-strain relation is assumed, and the material is assumed to harden in a kinematic fashion. Incremental loads are employed, and plastic loading, unloading, and reloading are all permitted.; There are three displacement and three force quantities at each end of the "plastica." For each loading increment at least three of these six quantities must be known in advance at both ends for the problem to be will-posed. With the known variables at one end and initial guesses of the unknown variables at the end, a shooting method combined with beam finite elements is used to predict the known (and unknown) variables at the other end. A Newton-type iteration scheme with finite-difference approximations to partial derivatives is then used to determine the variables at the initial end of the plastica, and to find the resulting configuration, internal forces, and reactions on the plastica for each loading increment.; Comparisons are made with numerical and analytical solutions to problems solved by others, and new examples are also included.
Engineering, Civil; Engineering, Mechanical
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/2142/716981988-01-01T00:00:00ZEffects of a Slow Gas-Phase Reaction on the L(*) Instability in Solid-Propellant Rockets
http://hdl.handle.net/2142/71697
Effects of a Slow Gas-Phase Reaction on the L(*) Instability in Solid-Propellant Rockets
L*-instability stemming from the interaction between the thermal relaxation in the solid propellant and the bulk-mode gas motion inside the combustion chamber is examined theoretically and numerically. The explosion reaction, following the quasisteady fizz reaction occurring near the burning surface, is analyzed for its unsteadiness and strong dependence on the chamber pressure and pressure transient. For this purpose, the asymptotic analysis exploiting the large activation energy of the explosion reaction is performed. The linear-stability results show that a system becomes more unstable due to the nonvanishing induction length in comparison with the quasisteady-flame limit, in addition to capturing all the trends for L*-instability obtained by the quasisteady flame theories. The current dp/dt-extinguishment criterion seems better in predicting the extinction trends in a low-pressure range than those obtained by quasisteady flame theories. By numerically solving the problem, large-amplitude, low-frequency oscillations are found to be associated with repeated extinctions and reignitions of the explosion reaction. In addition, the incomplete combustion is explained and many of the known extinction phenomena under high depressurization are captured. On the other hand, the unsteady process at the subsurface is pointed out as a possible cause for the chuffing.
Applied Mechanics; Engineering, Aerospace; Engineering, Mechanical
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/2142/716971988-01-01T00:00:00ZSome Aspects of the Mechanics and Mechanisms of Dynamic Brittle Fracture
http://hdl.handle.net/2142/71694
Some Aspects of the Mechanics and Mechanisms of Dynamic Brittle Fracture
Previous research in dynamic fracture mechanics has focused largely on steady-state growth in the absence of reflected stress waves. This is because of the analytical and experimental complexities of studying crack propagation in finite geometries. For example, inadequate spatial and temporal resolution is one potential limitation of high-speed photography, as used in the method of caustics, and in dynamic photoelasticity.; This study represents a major departure from current research. The problem chosen is that of brittle fracture in a finite-length beam under quasi-static flexure. The gradient stress field and boundary wave reflections present in this configuration lead to highly transient propagation which includes several intermittent arrests. Using newly developed optical methods, such as the Stress Intensity Factor Tracer (SIFT), dynamic stress intensity factor (K) and crack-tip velocity (v) have been measured continuously during fracture without using high-speed photography. The velocity-dependent fracture toughness relation, or K-v curve, has been obtained from a single specimen containing multiple run-arrests. Tests were conducted on PMMA (Plexiglass), an acrylic thermoset, and Homalite-100, a polyester resin, in their glassy states. The results for PMMA highlight the problems of characterizing history-dependent crack growth in rate-sensitive materials. The strong inertia effects observed during fracture were caused by boundary reflections of the unloading extensional waves and the Rayleigh surface waves emitted at fracture. Macroscopic measurements were supported by extensive fractography to gain insight into the mechanisms.; Several related aspects are also examined. A theoretical and experimental analysis of coherent light caustics for a Mode-I crack is presented in chapter 2. Errors in K estimation due to incorrect definitions of caustic diameter location caused by diffraction effects are discussed. Chapter 3 describes a sensitivity study of the SIFT method under quasi-static loading, to experimental variables like specimen geometry, notch root radius/near-tip effects, and focal plane aperture design. Also included is an extension of the SIFT focal plane mapping theory to characterize the Hutchinson-Tice-Rosengren singularity field for a stationary crack in power-law hardening materials. Chapter 4 provides an overview of critical issues concerning near-tip processes in dynamic fracture versus far-field characterization.
Applied Mechanics
Thu, 01 Jan 1987 00:00:00 GMThttp://hdl.handle.net/2142/716941987-01-01T00:00:00ZNumerical Analysis of the Effects of Void Growth and Crack Tip Opening on Ductile Fracture
http://hdl.handle.net/2142/71696
Numerical Analysis of the Effects of Void Growth and Crack Tip Opening on Ductile Fracture
The ductile rupture of metal alloys depends on the presence of small second phase particles which nucleate microscopic voids. Plastic flow in the metal allows the voids to grow and link up to create larger flaws such as cracks. In previous research, the basic mechanics of ductile fracture has been examined using two-dimensional models. However, some problems in ductile fracture are inherently three-dimensional. In this work three such problems are solved using large deformation finite element computations.; First, the finite element technique was used to study the growth of initially spherical voids in a cubic array under remote uniform loads of uniaxial tension, pure shear and high triaxial stress. The results show that shape change has a strong effect on the material's behavior. Indeed for low triaxial stress states, the effect of voids on the material response is stronger than expected due to void elongation. For higher triaxiality, the voids interact strongly to cause rapid drops in the material's load carrying capacity.; The second problem examines the effects of tip blunting and differential thinning on a crack in a thin elastic-plastic sheet. The finite element results show that two shear bands at 45 degrees to the plane of the sheet develop. Also, the results indicate the stresses are significantly higher in the near tip region at the midplane of the sheet than predicted by plane stress theory.; Finally, the growth and interaction of an array of initially spherical voids ahead of a blunting plane strain crack tip were studied. The finite element results show that spherical voids grow towards the crack tip and coalesce with the crack before they coalesce with each other. Increases in plastic strain were observed in the near tip region due to the presence of the voids. The results are used to discuss ductile crack growth in engineering alloys.
Engineering, Mechanical
Fri, 01 Jan 1988 00:00:00 GMThttp://hdl.handle.net/2142/716961988-01-01T00:00:00ZApplications of the Optical Method of Caustics to the Study of Viscoelastic Dynamic Fracture and Static Blunt Crack Fronts
http://hdl.handle.net/2142/71695
Applications of the Optical Method of Caustics to the Study of Viscoelastic Dynamic Fracture and Static Blunt Crack Fronts
The opto-mechanical relation, as used in the optical methods of photoelasticity and caustics, are extended to linearly viscoelastic materials. The Maxwell-Neumann relation for the stress-optic constants, which is good for linearly elastic behavior, is replaced by an expression derived from the Clausius-Mosotti-Lorentz-Lorenz (CMLL) equation. The opto-mechanical relation is given explicitly in terms of the mechanical and dielectric properties of the material. In the limiting case of elastic behavior, the present result is consistent with the Maxwell-Neumann relation. Approximations to the CMLL equation are discussed and compared with experiment.; The derived opto-mechanical relations are applied to the steady-state propagation of a crack in a viscoelastic material. Numerical computation of the caustic and initial curves are performed. The caustic shape changes very little from the elastic case. However, the size is dependent on the crack speed and temperature of the material.; Numerical calculations are used to determine the stress intensity factors of previously performed crack propagation experiments. The dynamic fracture toughness for Homalite 100 shows a strong temperature dependence for temperature variations below the glass transition temperature. Also, the crack branching toughness shows no dependence on temperature or crack speed and remains constant within the limits of the experimental error.; In order to address the accuracy and validity of the experimental measurement of the stress intensity factor, the stress field for a static blunt crack tip is investigated. The stress field surrounding a keyhole crack is given in terms of the eigenfunctions for a sharp crack. The eigenfunction stress field expansion for the keyhole crack contains additional coefficients of higher singularity than the usual square root singularity. The coefficients are determined by the boundary collocation method, which truncates the infinite series to satisfying the traction-free boundary condition on the face of the keyhole crack. The stress field is checked experimentally using the method of caustics. Numerically generated caustics are computed from the derived stress field. The caustic shapes compare well with experiment. The validity of using the caustic diameter alone to determine the stress intensity factor is discussed. The aspect ratio of the caustic appears to be a good indicator of the accuracy of the stress intensity factor measurement.
Applied Mechanics
Thu, 01 Jan 1987 00:00:00 GMThttp://hdl.handle.net/2142/716951987-01-01T00:00:00ZPostbuckling Analysis of Delaminated Composite Plates Under Compression (Composite Laminates)
http://hdl.handle.net/2142/71691
Postbuckling Analysis of Delaminated Composite Plates Under Compression (Composite Laminates)
Failure mechanics of delamination problems in composite laminates under compression is investigated. The failure modes in general may include prebuckling, postbuckling, delamination growth and final failure. Buckling load is determined by solving an eigenvalue problem using a subspace iteration technique. The Riks-Wempner iterative scheme is then used to determine the associated postbuckling load-displacement path. Owing to local buckling of the delaminated ligament, interlaminar stress transfer and strong material anisotropy, the singular stress field near the crack-tip must be considered for crack stability study. A rotational, singular hybrid finite element approach is taken for studying crack-tip stresses during postbuckling. Formulation of the element stiffness matrix is based on the assumption of small strain, large rotation and the recently developed laminate elasticity solution. The variational principle of a modified hybrid functional is employed for derivation of equilibrium equations in each incremental step. Comparisons of the results obtained from the present method and conventional finite elements are made to demonstrate the accuracy and efficiency of the present approach. Influences of eigenfunction truncation, and size of the rotational singular hybrid element on solution accuracy and convergence are studied. An analysis of symmetric graphite-epoxy composite laminates subjected to in-plane compression is attempted. Effects of fiber orientation and crack length on buckling instability and postbuckling behavior are studied. Mixed-mode stress intensity factors in delaminated (theta)/-(theta)/-(theta)/(theta) composite systems are calculated during postbuckling. Based on a critical mode-I fracture criterion, delamination stability is also investigated.
Engineering, Aerospace
Wed, 01 Jan 1986 00:00:00 GMThttp://hdl.handle.net/2142/716911986-01-01T00:00:00Z