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结合线弹性梁系有限元法和弹性模量缩减法,提出了梁系结构上限极限的分析方法。该方法根据构件截面广义屈服准则定义了梁系结构的单元承载比,得到了弹性模量缩减法的模量调整策略,利用梁系有限元法构造出了逼近极限状态的广义应力场以及系列机动允许位移场;同时推导出考虑弯矩和轴力共同影响下的梁单元弹性应变能和塑性耗散功计算公式,建立了梁系结构上限荷载乘子迭代算法。该算法继承了弹性模量调整法原理简单、应用方便等优点,并可应用于具有不同几何特性和材料特性构件构成的复杂结构中。算例分析表明:本文算法具有良好的计算精度和迭代稳定性,通常可在30个线弹性迭代步以内得到与解析法或其他算法在4%以内的极限分析结果。 相似文献
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假设功能梯度材料为一理想弹塑性材料,其弹性模量和屈服强度沿梁高度方向按照幂函数变化,在小变形及平截面假设下研究功能梯度材料纯弯曲梁的弹塑性性能.根据Mises屈服准则导出了纯弯曲梁的弹性极限弯矩的解析表达式,建立了梁在弹塑性状态时截面弯矩与截面弹、塑性区分布之间的关系式,给出了梁进入塑性极限状态时中性轴的位置以及塑性极限弯矩的解析计算公式.数值算例的结果表明,功能梯度材料梁的弹塑性性能与均匀材料梁不同,其屈服不一定首先产生于截面最大应力点,而可能有多种不同的屈服模态及相应的塑性扩展.弹性模量及屈服强度的梯度变化对功能梯度材料纯弯曲梁的中性轴位置、截面弹塑性应力分布以及塑性极限弯矩均有较大影响.研究结果可为功能梯度材料梁的弹塑性分析提供一定的参考. 相似文献
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假设功能梯度材料为理想弹塑性材料,其屈服强度和弹性模量均沿梁的高度方向按任意光滑函数连续变化,在小变形及平截面假定下,导出了功能梯度材料纯弯曲梁弹性极限弯矩及塑性极限弯矩的解析表达式,建立了弹塑性应力状态下截面弯矩和截面的弹、塑性应力分布之间的解析关系.研究表明,功能梯度材料梁存在多种可能的屈服模式,其最先屈服的点不一定位于截面应力最大处,而可能位于截面的其他任意位置;屈服强度及弹性模量的梯度变化对梁的弹塑性力学性能有很大影响.研究结果可为功能梯度材料纯弯曲梁的弹塑性问题研究提供一定的参考. 相似文献
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求解冷弯开口薄壁截面短柱的极限承载力是一个板组结构的大挠度弹塑性分析问题,板件之间相互作用和纵向面内加载方式对其局部屈曲后性能和稳定极限承载力有很大的影响。本文应用大挠度弹塑性有限条分析方法系统地研究了冷弯薄壁槽形截面柱的极限承载能力和它们的优化性能,并对荷载偏心距为常数和位移梯度为常数的两种加载条件下的薄壁开口短柱局部屈曲后性能和极限承载力进行了对比分析和探讨。 相似文献
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薄壁钢管再生混凝土轴压实验研究 总被引:3,自引:0,他引:3
通过对9个薄壁圆钢管再生混凝土短柱和9个薄壁方钢管再生混凝土短柱进行的轴压试验研究,比较了三种方法测定试件轴向变形的差异,分析了不同取代率和不同截面形式薄壁钢管再生混凝土的破坏变形特征,并运用不同设计规程对薄壁钢管再生混凝土的承载力强度进行了计算分析。得出薄壁钢管再生混凝土的变形破坏形式与普通薄壁钢管混凝土相似,及再生混凝土取代率对试件极限承载力和变形能力有一定影响的结论。另外根据计算比较,得到各规程在计算薄壁钢管再生混凝土极限承载力时的适用性。 相似文献
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本文给出了用解析法求得非均质(具有环向增强材料层的)圆筒在内压作用下(图1),处于弹塑性、极限状态时解的方法。为此,把弹性模量和屈服极限均表示为圆筒半径r的函数,将它们沿半径方向的变化规律用Fermi-Drac广义函数序列来表征。这一计算模式,不仅能够描述增强材料对于圆筒刚度的增强及其对于抗屈服能力的提高作用;而且还可以描述增强材料和基材间的弹性模量、屈服极限的连续变化规律。特别是对于不可压缩固体的这种非均质解,此方法就显得更为简便些。 相似文献
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Lufeng Yang Bo Yu Yong ping Qiao 《Acta Mechanica Solida Sinica》2009,22(2):109-115
A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio (EBR),and the elastic modulus reduction method (EMRM) is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method. 相似文献
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The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson’s ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape. 相似文献
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考虑剪切效应,利用切比雪夫多项式构造严格满足表面切应力边界条件的轴向位移表达式,建立了短梁弯曲问题的新理论.利用奇异函数把作用在短梁上的复杂外载荷表示为分布载荷,推导出了短梁弯曲时的截面正应力公式及挠曲线表达式.把采用切比雪夫多项式推导出短梁的弯曲计算公式计算结果与弹性理论计算结果进行比较,可知该方法的计算精度较高.研究结果表明:在复杂外载荷作用下,当长高比小于等于6时,剪切变形对梁的弯曲挠度影响较大,而当长高比小于3时,剪切变形对梁的弯曲应力影响较大;因此建议采用切比雪夫多项式方法给出的挠度表达式、弯曲应力进行计算,因为切比雪夫多项式方法不但给出了复杂外载荷作用下梁截面挠度、弯曲应力的计算通式,而且该方法具有计算过程简便、精度高的优点. 相似文献
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由基模态构造任意支撑杆的多项式型轴向刚度 总被引:1,自引:0,他引:1
给出了当杆的横截面积均匀而材料线密度为已知多项式时,由基模态构造任意支撑方式下杆的多项式型的轴向刚度系致的方法,证明了所得轴向刚度的正值性. 相似文献
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以截面形式、截面长宽比和混凝土类型为参数共设计了8根矩形中空夹层钢管混凝土试件,对其进行轴压实验并对其破坏形态、荷载-纵向应变关系曲线及外钢管横向应变发展规律进行分析。其中截面形式包括矩形套矩形和矩形套圆形两种,截面长宽比分别为1.25和1.5,混凝土类型包括普通混凝土和再生混凝土(再生粗骨料取代率为50%)两类。结果表明:对于截面形式相同的试件,长宽比较大者极限承载力更小,且其长边横向应变发展更快;对于长宽比相同的试件,矩形套矩形截面的试件长边横向应变发展比矩形套圆形截面的更快;混凝土类型对试件的极限承载力和破坏形态影响不大。最后运用有限元软件ABAQUS对8根短柱的轴压全过程进行模拟,并将有限元计算得到荷载-纵向应变曲线与实验实测曲线进行对比,两者吻合较好且互相验证。 相似文献
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Trabecular bone with its porous structure is an important compressive load bearing member. Different structural factors such
as porosity, non-homogeneous deformation, varying trabeculae thickness, connectivity, and nanoscale (10 nm to 1 μm) to macroscale
(~0.1 mm to 10 mm) composition hierarchy determine the failure properties of trabecular bone. While the above factors have
important bearing on bone properties, an understanding of how the local nanoscale properties change at different macroscale
compressive strain levels can be important to develop an understanding of how bone fails. In the present work, such analyses
are performed on bovine femoral trabecular bone samples derived from a single animal. Analyses focus on measuring nanoindentation
elastic moduli at three distinct levels of compressive strains in the bone samples: (1) when the samples are not loaded; (2)
after the samples have been loaded to a strain level just before apparent yielding and the macroscale compression test is
stopped; and (3) after the samples have been compressed to a strain level after apparent yielding and the macroscale compression
test is stopped. Nanoindentation elastic modulus values are two orders of magnitude higher than the macroscale compressive
elastic modulus values of all samples. A high variability in macroscale compressive elastic modulus values is observed because
of porous architecture and small sample size. Nanoindentation elastic modulus values show a progressive reduction with increase
in the extent of macroscale compressive deformation. Apparent yielding has a significant effect on this trend. The decrease
in nanoindentation modulus value for all samples accelerates from approximately 20% before yielding to approximately 60% after
yielding in comparison to the nanoindentation modulus values at 0% strain level. The level of variation in the predicted nanoindentation
modulus values is the lowest for uncompressed samples (~16–18%). However, with increase in the extent of compression, the
level of variation increases. It varied between 50% and 90% for the samples tested after yielding showing a widespread heterogeneity
in local nanoscale structural order after apparent yielding. Scanning electron microscope (SEM) observations suggest that
apparent yielding significantly destroys local nanoscale structural order. However, quantitative results suggest that a significant
residual nanoscale stiffness varying from 5 GPa to 8 GPa among different samples still remains for possible repair facilitation. 相似文献
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It is shown that some of the recently proposed orthotropic yield functions obtained through the linear transformation method are homogeneous polynomials. This simple observation has the potential to simplify considerably their implementation into finite element codes. It also leads to a general method for designing convex polynomial yield functions with powerful modeling capabilities. Convex parameterizations are given for the fourth, sixth and eighth order plane stress orthotropic homogeneous polynomials. Illustrations are shown for the modeling of biaxial and directional yielding properties of steel and aluminum alloy sheets. The parametrization method can be easily extended to general, 3D stress states. 相似文献