Optimal Shape and Nonhomogeneity of a Timoshenko Beam for Maximum Load

1979 ◽  
Vol 23 (04) ◽  
pp. 229-234
Author(s):  
Sarp Adali ◽  
Ibrahim Sadek
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Timoshenko Beam ◽  
Young's Modulus ◽  
Maximum Load ◽  
Optimal Shape ◽  
Graphical Form ◽  
Sectional Area ◽  
Cross Sectional ◽  
Closed Form Solutions

The best possible distributions of Young's modulus or the cross-sectional area or both are determined explicitly for a cantilevered Timoshenko beam which, for a given volume and end deflection, carries the maximum possible load at its free end. Closed-form solutions are given for the optimal height, width and/or Young's modulus functions. Numerical results are presented in graphical form. It is found that the inclusion of shear deformation decreases the efficiency of the optimal design, and that optimization with respect to Young's modulus in addition to shape increases the efficiency considerably in comparison with optimization of the shape only.

Effects of cross-sessional area and aspect ratio coupled with orientation on mechanical properties and deformation behavior of Cu nanowires

2021 ◽  
Author(s):  
Hui Cao ◽  
Wenke Chen ◽  
Zhiyuan Rui ◽  
Changfeng Yan
Keyword(s):  
Mechanical Properties ◽  
Aspect Ratio ◽  
Yield Stress ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Cu Nanowires ◽  
The Cross

Abstract Metal nanomaterials exhibit excellent mechanical properties compared with corresponding bulk materials and have potential applications in various areas. Despite a number of studies of the size effect on Cu nanowires mechanical properties with square cross-sectional, investigations of them in rectangular cross-sectional with various sizes at constant volume are rare, and lack of multifactor coupling effect on mechanical properties and quantitative investigation. In this work, the dependence of mechanical properties and deformation mechanisms of Cu nanowires/nanoplates under tension on cross-sessional area, aspect ratio of cross-sectional coupled with orientation were investigated using molecular dynamics simulations and the semi-empirical expressions related to mechanical properties were proposed. The simulation results show that the Young’s modulus and the yield stress sharply increase with the aspect ratio except for the <110>{110}{001} Cu nanowires/nanoplates at the same cross-sectional area. And the Young’s modulus increases while the yield stress decreases with the cross-sectional area of Cu nanowires. However, both of them increase with the cross-sectional area of Cu nanoplates. Besides, the Young’s modulus increases with the cross-sectional area at all the orientations. The yield stress shows a mildly downward trend except for the <111> Cu nanowires with increased cross-sectional area. For the Cu nanowires with a small cross-sectional area, the surface force increases with the aspect ratio. In contrast, it decreases with the aspect ratio increase at a large cross-sectional area. At the cross-sectional area of 13.068 nm2, the surface force decreases with the aspect ratio of the <110> Cu nanowires while it increases at other orientations. The surface force is a linearly decreasing function of the cross-sectional area at different orientations. Quantitative studies show that Young’s modulus and yield stress to the aspect ratio of the Cu nanowires satisfy exponent relationship. In addition, the main deformation mechanism of Cu nanowires is the nucleation and propagation of partial dislocations while it is the twinning-dominated reorientation for Cu nanoplates.

Harder than Diamond: Determining the Cross-Sectional Area and Young's Modulus of Molecular Rods

2005 ◽  
Vol 117 (45) ◽  
pp. 7598-7601 ◽  
Author(s):  
Lior Itzhaki ◽  
Eli Altus ◽  
Harold Basch ◽  
Shmaryahu Hoz
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Cross

scholarly journals MRI-based quantification of ophthalmic changes in healthy volunteers during acute 15° head-down tilt as an analogue to microgravity

2021 ◽  
Vol 18 (177) ◽  
Author(s):  
Stuart H. Sater ◽  
Austin M. Sass ◽  
Akari Seiner ◽  
Gabryel Conley Natividad ◽  
Dev Shrestha ◽  
...  
Keyword(s):  
Optic Nerve ◽  
Young’S Modulus ◽  
Structural Changes ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Fluid Shifts ◽  
Magnetic Resonance Imaging Mri ◽  
Ophthalmic Changes

Spaceflight is known to cause ophthalmic changes in a condition known as spaceflight-associated neuro-ocular syndrome (SANS). It is hypothesized that SANS is caused by cephalad fluid shifts and potentially mild elevation of intracranial pressure (ICP) in microgravity. Head-down tilt (HDT) studies are a ground-based spaceflight analogue to create cephalad fluid shifts. Here, we developed non-invasive magnetic resonance imaging (MRI)-based techniques to quantify ophthalmic structural changes under acute 15° HDT. We specifically quantified: (i) change in optic nerve sheath (ONS) and optic nerve (ON) cross-sectional area, (ii) change in ON deviation, an indicator of ON tortuosity, (iii) change in vitreous chamber depth, and (iv) an estimated ONS Young's modulus. Under acute HDT, ONS cross-sectional area increased by 4.04 mm 2 (95% CI 2.88–5.21 mm 2 , p < 0. 000), while ON cross-sectional area remained nearly unchanged (95% CI −0.12 to 0.43 mm 2 , p = 0.271). ON deviation increased under HDT by 0.20 mm (95% CI 0.08–0.33 mm, p = 0.002). Vitreous chamber depth decreased under HDT by −0.11 mm (95% CI −0.21 to −0.03 mm, p = 0.009). ONS Young's modulus was estimated to be 85.0 kPa. We observed a significant effect of sex and BMI on ONS parameters, of interest since they are known risk factors for idiopathic intracranial hypertension. The tools developed herein will be useful for future analyses of ON changes in various conditions.

Age-related differences in Achilles tendon properties and triceps surae muscle architecture in vivo

2012 ◽  
Vol 113 (10) ◽  
pp. 1537-1544 ◽  
Author(s):  
Lauri Stenroth ◽  
Jussi Peltonen ◽  
Neil J. Cronin ◽  
Sarianna Sipilä ◽  
Taija Finni
Keyword(s):  
Achilles Tendon ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Cross Sectional Area ◽  
Triceps Surae ◽  
Sectional Area ◽  
Cross Sectional ◽  
Tendon Stiffness ◽  
Triceps Surae Muscle ◽  
Age Related

This study examined the concurrent age-related differences in muscle and tendon structure and properties. Achilles tendon morphology and mechanical properties and triceps surae muscle architecture were measured from 100 subjects [33 young (24 ± 2 yr) and 67 old (75 ± 3 yr)]. Motion analysis-assisted ultrasonography was used to determine tendon stiffness, Young's modulus, and hysteresis during isometric ramp contractions. Ultrasonography was used to measure muscle architectural features and size and tendon cross-sectional area. Older participants had 17% lower ( P < 0.01) Achilles tendon stiffness and 32% lower ( P < 0.001) Young's modulus than young participants. Tendon cross-sectional area was also 16% larger ( P < 0.001) in older participants. Triceps surae muscle size was smaller ( P < 0.05) and gastrocnemius medialis muscle fascicle length shorter ( P < 0.05) in old compared with young. Maximal plantarflexion force was associated with tendon stiffness and Young's modulus ( r = 0.580, P < 0.001 and r = 0.561, P < 0.001, respectively). Comparison between old and young subjects with similar strengths did not reveal a difference in tendon stiffness. The results suggest that regardless of age, Achilles tendon mechanical properties adapt to match the level of muscle performance. Old people may compensate for lower tendon material properties by increasing tendon cross-sectional area. Lower tendon stiffness in older subjects might be beneficial for movement economy in low-intensity locomotion and thus optimized for their daily activities.

Optimal Design of a Nonhomogeneous Annular Disk Under Pressure Loadings

1994 ◽  
Vol 116 (4) ◽  
pp. 989-996
Author(s):  
Chung-Yun Gau ◽  
Souran Manoochehri
Keyword(s):  
Optimal Design ◽  
Young’S Modulus ◽  
Variable Thickness ◽  
Volume Fraction ◽  
Young's Modulus ◽  
Yield Criterion ◽  
Constant Thickness ◽  
Annular Disk ◽  
Disk Thickness ◽  
Thickness Variations

A method for the design of nonhomogeneous, variable-thickness, annular disks under internal and external pressures satisfying Tresca yield criterion is presented in this paper. The effects of varying the disk thickness and stiffness properties to achieve a fully stressed design are investigated. Analytical solutions for distributions of Young’s modulus and disk thickness variations have been developed for the case of fully stressed designs. Examples are given for three different cases, namely, constant thickness with variable Young’s modulus, variable thickness with constant Young’s modulus, and variable thickness with variable Young’s modulus. In the last case, due to the existence of many alternative solutions, optimal design techniques have been utilized. Application of the developed methodology for optimal designs of short fiber composites with random fiber orientations is discussed. The optimization results of fiber volume fraction distributions and thickness variations for a disk made of nylon 66 matrix with E glass fiber are given under specified pressure loadings.

Sign in / Sign up

Export Citation Format

Share Document