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THE GENERAL PURPOSE OF THIS STUDY WAS TO EVALUATE THE EFFICACY OF PERMITTING SIXTH- AND TWELFTH-GRADE STUDENTS TO ADOPT THEIR OWN WORK RATES DURING PROGRAMED INSTRUCTION. SPECIFIC COMPARISONS WERE MADE BETWEEN LOW- AND HIGH-ABILITY STUDENTS WORKING (1) UNDER SELF-PACED VERSUS FIXED-PACED CONDITIONS AND (2) IN GROUP SETTINGS VERSUS ISOLATED SETTINGS. AT BOTH GRADE LEVELS, THE HIGH-ABILITY STUDENTS PERFORMED SUPERIOR TO LOW-ABILITY STUDENTS. GROUP SETTINGS LED TO SLOWER, SELF-ADOPTED WORK RATES AND LOWER PROGRAM ERROR RATES THAN DID THE ISOLATED SETTINGS. HOWEVER, SETTING HAD NO RELIABLE EFFECT ON POST-TEST OR RETENTION SCORES. THE SELF-ADOPTED WORK RATES WERE HIGHLY STABLE ON TWO PROGRAMS. IT WAS CONCLUDED THAT THE ASSUMPTIONS UNDERLYING THE ADMINISTRATIVE STRATEGY CALL FOR SELF-PACING BECOME BETTER JUSTIFIED AT HIGHER GRADE LEVELS. TWELFTH-GRADERS ADOPTED WORK RATES WHICH CORRESPONDED CLOSELY WITH THEIR ABILITY. SIXTH GRADERS, HOWEVER, ADOPTED WORKRATES WHICH DID NOT CORRESPOND WELL WITH THEIR ABILITY AND WHICH OFTEN WERE EITHER TOO FAST OR TOO SLOW TO PERMIT EFFICIENT LEARNING. REMEDIAL COURSES OF ACTION WERE SUGGESTED. IT WAS RECOMMENDED THAT FUTURE RESEARCH BE DIRECTED TOWARD DETERMINING THE GENERALITY OF UNDERACHIEVEMENT RESULTING FROM MALADAPTIVE SELF-PACING STYLES, AND TOWARD DEVELOPING TECHNIQUES TO REMEDY SUCH STYLES. (JC)

This paper introduces a shape optimization of wire strands subjected to tensile loads. The structural analysis relies on a recently developed reduced helical finite element model characterized by an extreme computational efficacy while accounting for complex geometries of the wires. The model is extended to consider interactions between components and its applicability is demonstrated by comparison with analytical and finite element models. The reduced model is exploited in a design optimization identifying the optimal shape of a 1 + 6 strand by means of a genetic algorithm. A novel geometrical parametrization is applied and different objectives, such as stress concentration and area minimization, and constraints, corresponding to operational limitations and requirements, are analyzed. The optimal shape is finally identified and its performance improvements are compared and discussed against the reference strand. Operational benefits include lower stress concentration and higher load at plastification initiation., Advanced Modeling and Simulation in Engineering Sciences, 7 (1)

One of the advantages of corrugated laminates is that they show a significant increase in bending stiffness as the corrugation amplitude is increased. However, the change in transverse shear stiffness is expected to remain modest. In order to investigate said effects, an efficient (planar) finite element formulation has been derived which can be used to calculate the response of a corrugated laminate subjected to transverse shear loading. The results provided by the presented model highlight peculiarities in the resulting shear stress distribution. A special emphasis is laid on the difference between plates and corrugated structures, which is demonstrated by comparing the transverse shear stresses in flat laminates to corrugated laminates for different lay-ups.

Under the premise of homogeneous force, or curvature-gradient, distribution, a solution for transverse-shear strains and stresses, warping functions and through-thickness is derived by satisfying all relations and conditions of linear elasticity. Only for calculating the substitute-plate transverse-stiffness matrix the principle of the minimum of the total potential energy is used as a scheme for correctly combining energetically conjugate components of stresses and strains for the entries of the substitute-plate transverse stiffness matrix. The model is valid for all laminate and sandwich designs. The said premise renders the model a point theory rather than a structural theory, so that it is a complement to the classical theory of laminated plates in the sense of mapping substitute-plate properties and distribution of state variables through the laminate thickness. This paper explains the modeling ideas and derivations in detail. Predictions of the responses for a set of sample laminates of varying complexity, and comparison of stiffness values with those obtained by a dedicated FEM formulation, verify the model.

This paper contributes an analytical nonlinear morphing model for high-amplitude corrugated thinwalled laminates of arbitrary stack-up with a corrugation shape composed of circular sections. The model describes large deformations, the nonlinear relation between line force and global stretch, and the distribution of local line loads. The quarter-unit-cell approach together with assuming small material strains and a plane strain situation contribute to the model’s simplicity. It is explained how the solution procedure minimizes the force and moment residual of the equilibrium of cutting and reaction line loads by using Newton’s optimization method. Deformation results are verified by comparison with FEM simulation. The effects of laminate design and corrugation amplitude on deformations, line-force-stretch diagrams, and bending-curvature-stretch diagrams are presented and discussed., Curved and Layered Structures, 6 (1)

The axial and torsional response of helical bodies as well as their inner coupling has been in depth analyzed, both from an analytical and a numerical modeling perspective. Herein, the radial deformation is appended as an additional kinematic degree of freedom. To this end, an existing analytical theory is employed and advanced so as to account for radial strain. The extended stiffness matrix entries are further verified with the use of a finite element model over a wide range of helix angular configurations. Overall, closed-form expressions of the 3×3 structural response of the helical body are provided, relating axial, torsional and radial strain to their force and moment resultants.

THE RELATIVE EFFECTIVENESS OF ALTERNATE APPROACHES TOWARD INDIVIDUALIZATION OF FIXED-PACED PROGRAMED INSTRUCTION WAS ASSESSED. THIS REPRESENTED THE THIRD IN A SERIES OF THREE STUDIES CONCERNING THE RELATIONSHIP BETWEEN PACING MODE AND BEHAVIOR. (REFER TO ACCESSION NUMBERS ED 003 199, ED 003 200, AND ED 003 202 FOR ADDITIONAL INFORMATION ON THIS PROJECT.) PROGRAMED LESSONS IN SCIENCE WERE PRESENTED OVER TELEVISION TO EIGHTH-GRADE STUDENTS. A TOTAL OF 12 SEPARATE VERSIONS WERE COMPARED, INCLUDING 3 VERSIONS DIFFERING IN PROMPTING STRENGTH AND PRESENTED AT 4 DIFFERENT TEMPOS. COMPARISONS WERE MADE AMONG TREATMENTS FOR ERRORS, POST-TEST SCORES, AND RETENTION SCORES. WHILE ADDED PROMPTING DID REDUCE ERROR RATES, IT ALSO LED TO LOWER ACHIEVEMENT. ITS POTENTIAL VALUE IN OVERCOMING THE DETRIMENTAL EFFECTS OF FIXED PACING WAS DISCOUNTED. INTERACTIVE TRENDS WERE OBSERVED BETWEEN CHARACTERISTIC WORK RATES AND TEMPO VARIATIONS. MULTIPLE PROGRAM SOURCES WERE DISCUSSED AS MEANS FOR PROVIDING EFFECTIVE AND EFFICIENT GROUP INSTRUCTION. (JC)

Research supported by U.S. Office of Education, Bureau of Research, Project No. 5-1122, Grant No. OEG-1-6-051122-0583.

Due to their superior mass specific mechanical properties laminated composite structures are today well established for aircraft and spacecraft applications. The possibility to tailor the properties of laminates to local requirements at different regions of the structure is an additional advantage. The large number of design variables as well as the anisotropic behavior of the layers result in a complex and time consuming design process. The usage of an automated design procedure including an optimization can reduce these costs and lead to better solutions. Stress concentrations caused by cut outs or load introduction points may reduce the strength of a structure. These areas can be reinforced with local laminate doublers. Finding efficient doubler geometries is not trivial and hard to be done intuitively. Automated design processes can help improving solutions quality and reduce time costs. In contrast to eigenfrequencies buckling or compliance strength is a local phenomenon. Considering non homogeneous stress states the strength of the structure is restricted by the maximum stresses. Allowing locally varying laminates a design change may cause a sudden relocation of the critically stressed region what leads to a non differentiable objective function. Gradient based optimization algorithms cannot be applied and stochastic algorithms are often used instead. In this paper a differentiable pseudo objective function is introduced that unites the failure indices of the structure. This enables the determination of a gradient field that expresses the influence of a layer thickness change on the strength. It is later used to generate reinforcement doublers starting from an unreinforced initial design. Material is added step wise based on gradient information until a required strength is reached. Since weight is linearly depending on the layer thicknesses the placement of the reinforcements is very efficient in terms of mass.

ECCM 14 : 14th European Conference on Composite Materials : June 7 - 10, 2010, Budapest, Hungary

Composite materials are established as reliable and efficient materials for a large number of structural applications. Although composites have gained widespread use, we do not, as of yet, have a precise and complete understanding of the mechanismsm of damage development in composite materials. Recent research results have pointed out the need to treat damage as a collective condition; i.e., a damage state, rather than as an assembly of discrete and independent damage modes. The process of the development of the damage state and the subsequent response of the composite laminate throughout the loading history can then be related. This report presents the results of an investigation to determine the damage states which develop in graphite epoxy laminates with center holes due to tensio-tension cyclic loads, to determine the influence of stacking sequence on the initiation and interaction of damage modes and the process of damage development, and to establish the relationships between the damage states and the strength, stiffness, and life of the laminates., Two quasi-isotropic laminates were selected to give different distributions of interlaminar stresses around the hole. The laminates were tested under cyclic loads (R=0.1, 10 Hz) at maximum stresses ranging between 60 95 percent of the notched tensile strength. Damage was monitored nondestructively throughout the loading history using stereo X-ray radiography, acoustic emission recording, and stiffness change. Some specimens were deplied after specific numbers of cycles to determine the nature and distribution of damage in each ply araound the hole and to confirm the components and size of the damage state observed nondestructively. Fatigue life and residual strength tests were also performed. Fatigue damage in the two laminates included matrix cracks in all plies followed by delaminations. The density of matrix cracks and the distribution of the damage zone (matrix cracks plus delaminations) in laminates cycled at the same percent of notched tensile strength were strongly dependent on the local constraint and distribution of interlaminar stresses as governed by the stacking sequence. The distinctly different damage states which developed in the two initially quasi-sitropic laminates due to similar load histories produced stiffness changes of 15-20 percent, different rates of residual strength degradation, and a factor of four difference in fatigue life. The results of this study are interpreted to establish relationships between the loading history, the progressive development of the damage state, and the response of the notched laminates.

Changes in the stiffness and strength of notched quasi-isotropic graphite-epoxy laminates were recorded and related to the fatigue damage. Two different laminates [0,90,+45,-45]s (type A) and [ +45, 90, -45, 0] s (type B) were considered and the effects of stacking sequence were compared. Nondestructive testing techniques such as X-radiography, moire technique, acoustic emission, deply technique, and stiffness change were performed to observe damage development. Static properties and damage initiation were related to an approximate stress analysis. Results show that the mechanical response and the fatigue damage depend strongly on the stacking sequence of laminates. In general, residual strength increased remarkably for both laminates due to stress redistributions while the continuous stiffness change curve is typical for each laminate and reflects damage characteristics. Buckling effects as well as matrix cracking and delaminations contribute to stiffness changes. M.S.