Showing papers on "Stiffness published in 1980"

Analysis and Performance of Fiber Composites

Abstract: Preface. 1 Introduction. 1.1 Definition. 1.2 Characteristics. 1.3 Classification. 1.4 Particulate Composites. 1.5 Fiber-Reinforced Composites. 1.6 Applications of Fiber Composites. Exercise Problems. References. 2 Fibers, Matrices, and Fabrication of Composites. 2.1 Advanced Fibers. 2.1.1 Glass Fibers. 2.1.2 Carbon and Graphite Fibers. 2.1.3 Aramid Fibers. 2.1.4 Boron Fibers. 2.1.5 Other Fibers. 2.2 Matrix Materials. 2.2.1 Polymers. 2.2.2 Metals. 2.3 Fabrication of Composites. 2.3.1 Fabrication of Thermosetting Resin Matrix Composites. 2.3.2 Fabrication of Thermoplastic-Resin Matrix Composites (Short-Fiber Composites). 2.3.3 Fabrication of Metal Matrix Composites. 2.3.4 Fabrication of Ceramic Matrix Composites. Suggested Reading. 3 Behavior of Unidirectional Composites. 3.1 Introduction. 3.1.1 Nomenclature. 3.1.2 Volume and Weight Fractions. 3.2 Longitudinal Behavior of Unidirectional Composites. 3.2.1 Initial Stiffness. 3.2.2 Load Sharing. 3.2.3 Behavior beyond Initial Deformation. 3.2.4 Failure Mechanism and Strength. 3.2.5 Factors Influencing Longitudinal Strength and Stiffness. 3.3 Transverse Stiffness and Strength. 3.3.1 Constant-Stress Model. 3.3.2 Elasticity Methods of Stiffness Prediction. 3.3.3 Halpin-Tsai Equations for Transverse Modulus. 3.3.4 Transverse Strength. 3.4 Prediction of Shear Modulus. 3.5 Prediction of Poisson's Ratio. 3.6 Failure Modes. 3.6.1 Failure under Longitudinal Tensile Loads. 3.6.2 Failure under Longitudinal Compressive Loads. 3.6.3 Failure under Transverse Tensile Loads. 3.6.4 Failure under Transverse Compressive Loads. 3.6.5 Failure under In-Plane Shear Loads. 3.7 Expansion Coefficients and Transport Properties. 3.7.1 Thermal Expansion Coefficients. 3.7.2 Moisture Expansion Coefficients. 3.7.3 Transport Properties. 3.7.4 Mass Diffusion. 3.8 Typical Unidirectional Fiber Composite Properties. Exercise Problems. References. 4 Short-Fiber Composites. 4.1 Introduction. 4.2 Theories of Stress Transfer. 4.2.1 Approximate Analysis of Stress Transfer. 4.2.2 Stress Distributions from Finite-Element Analysis. 4.2.3 Average Fiber Stress. 4.3 Modulus and Strength of Short-Fiber Composites. 4.3.1 Prediction of Modulus. 4.3.2 Prediction of Strength. 4.3.3 Effect of Matrix Ductility. 4.4 Ribbon-Reinforced Composites. Exercise Problems. References. 5 Analysis of an Orthotropic Lamina. 5.1 Introduction. 5.1.1 Orthotropic Materials. 5.2 Stress-Strain Relations and Engineering Constants. 5.2.1 Stress-Strain Relations for Specially Orthotropic Lamina. 5.2.2 Stress-Strain Relations for Generally Orthotropic Lamina. 5.2.3 Transformation of Engineering Constants. 5.3 Hooke's Law and Stiffness and Compliance Matrices. 5.3.1 General Anisotropic Material. 5.3.2 Specially Orthotropic Material. 5.3.3 Transversely Isotropic Material. 5.3.4 Isotropic Material. 5.3.5 Specially Orthotropic Material under Plane Stress. 5.3.6 Compliance Tensor and Compliance Matrix. 5.3.7 Relations between Engineering Constants and Elements of Stiffness and Compliance Matrices. 5.3.8 Restrictions on Elastic Constants. 5.3.9 Transformation of Stiffness and Compliance Matrices. 5.3.10 Invariant Forms of Stiffness and Compliance Matrices. 5.4 Strengths of an Orthotropic Lamina. 5.4.1 Maximum-Stress Theory. 5.4.2 Maximum-Strain Theory. 5.4.3 Maximum-Work Theory. 5.4.4 Importance of Sign of Shear Stress on Strength of Composites. Exercise Problems. References. 6 Analysis of Laminated Composites. 6.1 Introduction. 6.2 Laminate Strains. 6.3 Variation of Stresses in a Laminate. 6.4 Resultant Forces and Moments: Synthesis of Stiffness Matrix. 6.5 Laminate Description System. 6.6 Construction and Properties of Special Laminates. 6.6.1 Symmetric Laminates. 6.6.2 Unidirectional, Cross-Ply, and Angle-Ply Laminates. 6.6.3 Quasi-isotropic Laminates. 6.7 Determination of Laminae Stresses and Strains. 6.8 Analysis of Laminates after Initial Failure. 6.9 Hygrothermal Stresses in Laminates. 6.9.1 Concepts of Thermal Stresses. 6.9.2 Hygrothermal Stress Calculations. 6.10 Laminate Analysis Through Computers. Exercise Problems. References. 7 Analysis of Laminated Plates and Beams. 7.1 Introduction. 7.2 Governing Equations for Plates. 7.2.1 Equilibrium Equations. 7.2.2 Equilibrium Equations in Terms of Displacements. 7.3 Application of Plate Theory. 7.3.1 Bending. 7.3.2 Buckling. 7.3.3 Free Vibrations. 7.4 Deformations Due to Transverse Shear. 7.4.1 First-Order Shear Deformation Theory. 7.4.2 Higher-Order Shear Deformation Theory. 7.5 Analysis of Laminated Beams. 7.5.1 Governing Equations for Laminated Beams. 7.5.2 Application of Beam Theory. Exercise Problems. References. 8 Advanced Topics in Fiber Composites. 8.1 Interlaminar Stresses and Free-Edge Effects. 8.1.1 Concepts of Interlaminar Stresses. 8.1.2 Determination of Interlaminar Stresses. 8.1.3 Effect of Stacking Sequence on Interlaminar Stresses. 8.1.4 Approximate Solutions for Interlaminar Stresses. 8.1.5 Summary. 8.2 Fracture Mechanics of Fiber Composites. 8.2.1 Introduction. 8.2.2 Fracture Mechanics Concepts and Measures of Fracture Toughness. 8.2.3 Fracture Toughness of Composite Laminates. 8.2.4 Whitney-Nuismer Failure Criteria for Notched Composites. 8.3 Joints for Composite Structures. 8.3.1 Adhesively Bonded Joints. 8.3.2 Mechanically Fastened Joints. 8.3.3 Bonded-Fastened Joints. Exercise Problems. References. 9 Performance of Fiber Composites: Fatigue, Impact, and Environmental Effects. 9.1 Fatigue. 9.1.1 Introduction. 9.1.2 Fatigue Damage. 9.1.3 Factors Influencing Fatigue Behavior of Composites. 9.1.4 Empirical Relations for Fatigue Damage and Fatigue Life. 9.1.5 Fatigue of High-Modulus Fiber-Reinforced Composites. 9.1.6 Fatigue of Short-Fiber Composites. 9.2 Impact. 9.2.1 Introduction and Fracture Process. 9.2.2 Energy-Absorbing Mechanisms and Failure Models. 9.2.3 Effect of Materials and Testing Variables on Impact Properties. 9.2.4 Hybrid Composites and Their Impact Strength. 9.2.5 Damage Due to Low-Velocity Impact. 9.3 Environmental-Interaction Effects. 9.3.1 Fiber Strength. 9.3.2 Matrix Effects. Exercise Problems. References. 10 Experimental Characterization of Composites. 10.1 Introduction. 10.2 Measurement of Physical Properties. 10.2.1 Density. 10.2.2 Constituent Weight and Volume Fractions. 10.2.3 Void Volume Fraction. 10.2.4 Thermal Expansion Coefficients. 10.2.5 Moisture Absorption and Diffusivity. 10.2.6 Moisture Expansion Coefficients. 10.3 Measurement of Mechanical Properties. 10.3.1 Properties in Tension. 10.3.2 Properties in Compression. 10.3.3 In-Place Shear Properties. 10.3.4 Flexural Properties. 10.3.5 Measures of In-Plane Fracture Toughness. 10.3.6 Interlaminar Shear Strength and Fracture Toughness. 10.3.7 Impact Properties. 10.4 Damage Identification Using Nondestructive Evaluation Techniques. 10.4.1 Ultrasonics. 10.4.2 Acoustic Emission. 10.4.3 x-Radiography. 10.4.4 Thermography. 10.4.5 Laser Shearography. 10.5 General Remarks on Characterization. Exercise Problems. References. 11 Emerging Composite Materials. 11.1 Nanocomposites. 11.2 Carbon-Carbon Composites. 11.3 Biocomposites. 11.3.1 Biofibers. 11.3.2 Wood-Plastic Composites (WPCs). 11.3.3 Biopolymers. 11.4 Composites in "Smart" Structures. Suggested Reading. Appendix 1: Matrices and Tensors. Appendix 2: Equations of Theory of Elasticity. Appendix 3: Laminate Orientation Code. Appendix 4: Properties of Fiber Composites. Appendix 5: Computer Programs for Laminate Analysis. Index.

Active stiffness control of a manipulator in cartesian coordinates

Abstract: A method of actively controlling the apparent stiffness of a manipulator end effecter is presented. The approach allows the programmer to specify the three transnational and three rotational stiffness of a frame located arbitrarily in hand coordinates. Control of the nominal position of the hand then permits simultaneous position and force control. Stiffness may be changed under program control to match varying task requirements. A rapid servo algorithm is made possible by transformation of the problem into joint space at run time. Applications examples are given.

Optimum absorber parameters for simple systems

Abstract: In the classical problem a damped one degree-of-freedom absorber system is attached to a main system, which has one degree of freedom and is undamped The optimum values of absorber stiffness and damping, which will minimize the resonant response of the main mass, are well known In this paper the effect on these optimum conditions of light damping in the main system is studied The authors show that optimum parameters for absorbers, which are attached to beams and plates, can be obtained simply and accurately from those for an equivalent one degree-of-freedom main system This depends upon the concept of an effective mass for the elastic body and the representation of its response by the single relevant mode It will be shown in a later paper that for more complex elastic bodies such as cylindrical shells, for which the natural frequencies are more closely spaced, these simple concepts do not predict accurately optimum absorber parameters

Mechanical property distributions in the cancellous bone of the human proximal femur

Abstract: Proximal femurs obtained at routine autopsy were sectioned into large numbers of 5 mm cubic specimens, in order to obtain detailed quantitative information about the spatial and directional variations of the material properties of the cancellous bone. Low strain rate compression tests were performed, evaluating the apparent elastic modulus and yield strength, in three perpendicular testing directions, for each cube. A computer contouring program was used to assemble the experimental data into smoothed distribution plots across sections of interest.The results revealed stiffness and strength elevations/reductions which clearly correspond to roentgenographic features. Especially prominent stiffness elevations (160 to 400 percent above the overall cancellous bone average) were found in the regions traversed by the primary trabeculation system, although the modulus of the bone samples was substantially reduced when measured in directions other than those of habitual weight-bearing. Similar but less pronounced...

A Self-Consistent Approach to the Elastic Stiffness of Short-Fiber Composites

Abstract: The self-consistent approach originally proposed by Hill has been adopted to derive the effective elastic stiffness constants of unidirectional short-fiber composites. The short-fibers are modeled as ellipsoidal inclu sions uniformly distributed in the matrix and the transverse isotropy of the composite has been taken into account. The method of analysis is valid for multi-component systems and hence, applicable to hybrid composites. Comparisons of this analysis with existing theories are made for binary composites.

Evidence that the human jaw stretch reflex increases the resistance of the mandible to small displacements.

Abstract: 1. Small 'step' or sinusoidal displacements were imposed on the mandible while human subjects maintained an average biting force of 10 N. Phase-related changes in the force resisting sinusoidal displacement were used to determine the mechanical stiffness of the human mandibular system as a function of the frequency of stretching. 2. Jaw-muscle electromyographic (e.m.g.) responses to 'step' stretches were of 8 msec latency and generated a very substantial force response. Jaw-muscle e.m.g. responses having longer latency were not observed. 3. The mechanical stiffness of the human mandible was relatively constant as a function of the frequency of stretching, having a typical magnitude of about 15 N/mm (+/- 200 micrometers stretch) or 10 N/mm (+/- 1500 micrometers stretch) at mean biting forces of 10 N. The force resisting displacement was phase-advanced at all frequencies. 4. Modulation of jaw muscle electrical activity evoked by sinusoidal stretches increased in amplitude as a function of increasing stretch frequency. E.m.g. modulation was 60--100 degrees advanced at frequencies of 1--10 Hz, but the phase decreased at higher frequencies, becoming negative (lagging stretch) at frequencies of 30 Hz and above. These characteristics are consistent with the idea that the jaw stretch reflex is dependent on jaw muscle spindle afferent fibres exciting jaw-closing motoneurones by relatively direct (but not necessarily monosynaptic) connexions. 5. The relationship between jaw-muscle activity and voluntary fluctuations of isometric biting force suggests that human jaw muscles can be modelled as a second-order linear 'filter'. The corner frequency for human jaw muscle is about 3 Hz; thus it would appear to be considerably slower than jaw muscle of monkeys. 6. The reflex stiffness of the human mandible, estimated quantitatively on the assumption that human jaw muscle stiffness is similar to the intrinsic stiffness of the gastrocnemius of the cat, ranges between 5 and 9 N/mm at frequencies between 1 and 8 Hz. Since this reflex stiffness is about the same as muscle stiffness in this frequency range, we conclude that the stretch reflex of the human mandible contributes functionally to its postural stability. 7. Reflex stiffness appears to be greater in the monkey mandible relative to muscle stiffness than in the human mandible. The difference is argued to be a manifestation of the difference in jaw muscle contraction speed between the two species. 8. The fact that the mandibular stretch reflex appears to be stronger than the stretch reflex of the limbs of intact animals and humans is discussed in terms of the special anatomical and functional features of the mandible.

Finite elements based on energy orthogonal functions

Abstract: It is shown how the convergence requirements for a finite element may be written as a set of linear constraints on the stiffness matrix. It is then attempted to construct a best possible stiffness matrix. The constraint equations restrict the way in which these stiffness terms may be chosen; however, there is normally still room for improving or optimizing an element. It is demonstrated how an element stiffness matrix may be found using rigid body, constant strain and higher order deformation modes. Further, it is shown how the constraint equations may be exploited in deriving an ‘energy orthogonality theorem’. This theorem opens the door to a whole new class of simple finite elements which automatically satisfy the convergence requirements. Examples of deriving plane stress and plate bending elements are given.

A microstructure model for the rheology of mammalian tendon.

Abstract: The rheological behavior of mammalian tendon is analyzed in terms of its constituents structure and their properties. The elastic fibers are assumed to be straight and linearly elastic. They are of predominant role in the low ranges of strain. The collagen fibers are nonuniformly undulated. Upon stretch they gradually become straight, thus increasing the stiffness of the tissue. They are assumed to be linearly viscoelastic with negligible bending strength. It is shown that the nonuniformity of the collagen fiber structure can account for the observed nonlinear load-strain relations as well as for the nonlinear viscoelastic behavior of the tendon. An experimental procedure is developed through which the material functions and parameters can be determined.

Structural analysis of concrete pavement systems

Abstract: Performance of concrete pavements is controlled by the behavior and performance of the jointing system used, especially the performance and load transfer efficiency of the joint. A finite-element program is presented that includes the analysis of slabs with various joint systems in PCC pavements. Dowelled joints, joints with aggregate interlock, and joints with various types of load transfer schemes can be taken into account during the analysis of the slab under load rather than analyzing the slab and joint systems separately and superimposing the results. The program described is also capable of analyzing slabs comprised of two layers with different material properties, either bonded together or unbonded. Slab thickness, slab modulus values, and subgrade support values can each be varied at each node point in the program to evaluate jointed slabs of nonuniform stiffness and nonuniform support.

The Measurement of the Radial Stiffness of Rolling Element Bearings under Oscillating Conditions

Abstract: There is very little information available on the characteristics of rolling element bearings under oscillating conditions. This is because of the difficulty that has been experienced in measuring the relevant characteristics. A rig is described which is very simple in principle and allows the measurement of the radial stiffness of a pair of bearings. For the angular contact bearings tested the levels of damping obtained are larger than previously expected.

Steel wire foundation

Abstract: A foundation unit which, when assembled, can be collapsed for compact storage and shipping and later can be elevated to a fully expanded state. The foundation unit includes a rectangular, grid wire top bearing structure, a rigid bottom substructure such as a wooden frame, and a series of spaced, parallel rows of substantially flat support members extending between the top bearing structure and the bottom substructure. The support members are hingedly secured to the top bearing structure and bottom substructure to permit reduction of the foundation unit to the collapsed state with the rows of support members lying essentially prone. In the elevated state, the foundation unit includes stabilizers which are oppositely reactive and which prevent relative longitudinal translation between the top and bottom of the foundation unit. Depending on the firmness characteristics required of the foundation unit, the flat support members can assume one of a number of different configurations, offering total stiffness or varying degrees of recoilable compression of the foundation unit.

Dynamic and Static Properties of Recessed Hydrostatic Journal Bearings by Small Displacement Analysis

Abstract: Coefficients are presented for hydrostatic stiffness, hydrodynamic stiffness and squeeze damping for capillary, orifice and constant flow control. Due to the linear behaviour of such bearings these coefficients may be used for conservative design and with reasonable accuracy where the displacements are less than half the clearance. The dynamic coefficients may also be employed to predict the onset of whirl. The results are illustrated by application to rotating and non-rotating load situations. It is demonstrated that the squeeze damping constant for the concentric condition may be obtained from a steady loading test for hydrodynamic stiffness since Csq = λhd /(πN). It is argued that this relationship may be generalised for all types of bearings capable of exhibiting half-speed whirl operating at any speed.

Finite elements with penalties in nonlinear elasticity

Abstract: This paper describes the use of a penalty method to enforce the constraint of incompressibility in nonlinear elasticity. As an example, a problem involving the use of the Newton–Raphson method in conjunction with incremental loading and a successive mesh refinement scheme is presented. It is shown that during the incremental loading phase and the Newton–Raphson refinement on a fixed mesh, all tangent stiffness matrices are positive definite for the chosen energy density and load increment. But when the mesh is refined and the solution is interpolated as a starting value on the new mesh, the tangent stiffness matrix is indefinite. A theoretical analysis of the associated mixed method and a new equivalence theorem are seen to lead to a way to retain positive definiteness. The key is the use of an equivalent tangent stiffness matrix which is the reduced Hessian matrix. The numerical example shows that both positive definiteness and the quadratic convergence rate of the Newton–Raphson method are obtained.

Stiffness Change as a Nondestructive Damage Measurement

Abstract: In laboratory specimens, damage growth is generally accompanied by stiffness change. Hence, damage growth can be monitored indirectly through stiffness. Furthermore, stiffness measurements are both nondestructive and easier to apply than most NDI methods that measure damage directly. This paper highlights laboratory applications of stiffness measurement for indirect assessment of damage growth and, in some special cases, for failure prediction. Examples cited are buckling of compressively loaded cylindrical shells, slow stable crack growth in tension-loaded notched coupons, fatigue-crack growth in adhesively bonded materials, and fatigue-damage growth in composite materials.

Further Consideration of Progressively Fracturing Solids

Abstract: A material idealization in which degradation of stiffness leads to nonlinear behavior and strain softening is described. Such a model may have applications with materials such as nonwoven fabrics, rocks, concrete, etc. The theory is developed partly by analogy with the theory of hardening plasticity, and completed by establishing how the change of stiffness can be found for any given history of deformation. Examples are given with the idealization being used to obtain results for a two-dimensional, sheet-like, material subjected to a variety of deformation paths. These illustrate the principal features of the model including softening, strain induced anisotropy, and dilatancy.

Symmetricability of pressure stiffness matrices for shells with loaded free edges

Abstract: For the case of free edges which are loaded, follower forces remaining normal to the middle surface of a shell throughout the deformation history do not have a load potential. In finite element analysis, this results in an unsymmetric pressure stiffness matrix. Depending on the structure of the available computer program, implementation of an equation solver permitting solution of unsymmetric simultaneous systems of algebraic equations may be a tedious task. This explains the significance of the topic of symmetricability of pressure stiffness matrices, turning out to be of special importance in the case of static buckling under the assumption of a linear prebuckling path. At first, incremental equations for tracing the nonlinear load–displacement path are derived. Thereafter, the buckling condition is deduced. Then, it is demonstrated that symmetrization of the pressure stiffness matrix is admissible if the so-obtained ‘buckling pressure’ differs ‘very little’ from the ‘buckling pressure’ resulting from an alternative symmetric ‘buckling matrix’, as is shown to be the case for a simply supported cylindrical shell with a free upper edge, subjected to hydrostatic external pressure. The alternative symmetric ‘buckling matrix’ is a consequence of deleting the virtual work term, causing the unsymmetry of the pressure stiffness matrix, in the expression for the external virtual work. A mechanical interpretation of this virtual work term is given. It is shown to be equal to the difference of virtual work of the original pressure load and of a ‘substitute pressure-field’, of the form of a Fourier series of the former. This explains why, normally, the buckling coefficient resulting from the ‘substitute pressure-field’ represents a good approximation to the buckling coefficient stemming from the original pressure load.

Dynamic stiffness and seismic response of sleeved piles

Abstract: An axisymmetric finite element formulation with a consistent transmitting boundary is used to obtain dynamic stiffnesses and seismic response of sleeved piles in linear viscoelastic soil media. A sleeved pile consists of a column within a sleeve of substantially larger diameter which is filled with concrete to some depth below grade level. Recent research on the behavior of pile-foundations under dynamic loads has been stimulated by dynamic behavior studies which have disclosed that the effects study: a finite element formulation with a consistent transmitting boundary to stimulate the soil medium encircling the pile, and an approximate analytical method based on the concept of a generalized Winkler medium. Form the approximate analytical method, closed-form expressions were derived for the dynamic stiffness of the piles. Comparison of the results of the analytical and the finite element formulation methods showed that the analytical method, together with the appropriate subgrade moduli also obtained in this study, provide fairly accurate results for dynamic stiffnesses at low as well as at high frequencies.

Steel-polypropylene-steel laminate: a new weight reduction material

Abstract: The dent resistance, flexural stiffness, fatigue strength, and formability are characterized for a steel-polypropylene-steel (S-P-S) laminate for automotive applications. Many of these physical properties are comparable to those of steel. The S-P-S laminate takes advantage of the I-beam principle in bending. The highest stress is in the surface, with the lowest stress at the neutral axis. The material has a high stiffness-to-weight ratio, with the potential to reduce component weight by 50% with no loss in flexural stiffness. Applications where bending stiffness is the major design criterion include: seat backs, load floors, covers, narrow body panels, truck trailer sides, and interior trim. One disadvantage of S-P-S is loss of bolt torque due to creep by the polypropylene core. This loss is a function of the applied stress level, core thickness and temperature.

In-Plane Vibration and Buckling of a Rotating Beam Clamped Off the Axis of Rotation

Abstract: Some work on the in-plane vibrations and buckling of rotating beams, clamped off the axis of rotation, is unclear as to behavior in the limit of small stiffness and small off-clamping. In this paper, asymptotic expansion formulas are developed for both small and large values of stiffness and off-clamping parameters. A composite expansion formula is also introduced as an engineering approximation to the buckling curve for all values of parameters. The present results agree quite well with an exact numerical solution and indicate that buckling can occur for arbitrarily small stiffness and off-clamping.