西北工业大学学报
西北工業大學學報
서북공업대학학보
JOURNAL OF NORTHWESTERN POLYTECHNICAL UNIVERSITY
2013年
4期
624-628
,共5页
高阶位移场%正交各向异性%圆柱壳%多孔金属材料
高階位移場%正交各嚮異性%圓柱殼%多孔金屬材料
고계위이장%정교각향이성%원주각%다공금속재료
errors%finite element method%homogenization method%matrix algebra%schematic diagrams%strain%strain energy%variational techniques%cylindrical tube%higher-order displacement field ( HODF) theo-ry%lattice structure%orthotropic material
基于高阶位移场理论研究了简支条件棱镜型圆柱壳体在内压力作用下的结构响应。首先,建立承受内压圆柱壳体的平衡方程,计算在该载荷作用下的各项同性材料的响应,与弹性力学理论解进行对比,验证所得平衡方程的正确性。采用均匀化方法,将正方形,三角形和Kagome 3种多孔金属圆柱壳体等效为正交各向异性的材料,计算了在内压下的结构响应,并与有限元计算结果进行对比,结果表明文中方法所得结果与有限元的结果非常接近,计算得到的径向位移和轴向应变与有限元的计算基本相同,径向应力,环向应力和径向应变等结构响应时误差也较小。3种构型的计算结果与有限元计算结果的比值变化趋势基本相同,其中三角形和Kagome构型的计算结果较正方形构型的计算结果较为准确。通过对所得结果进行分析,可以发现该高阶位移场理论在计算圆柱壳体结构响应时有效、准确,可以作为预测该类结构响应的计算方法。
基于高階位移場理論研究瞭簡支條件稜鏡型圓柱殼體在內壓力作用下的結構響應。首先,建立承受內壓圓柱殼體的平衡方程,計算在該載荷作用下的各項同性材料的響應,與彈性力學理論解進行對比,驗證所得平衡方程的正確性。採用均勻化方法,將正方形,三角形和Kagome 3種多孔金屬圓柱殼體等效為正交各嚮異性的材料,計算瞭在內壓下的結構響應,併與有限元計算結果進行對比,結果錶明文中方法所得結果與有限元的結果非常接近,計算得到的徑嚮位移和軸嚮應變與有限元的計算基本相同,徑嚮應力,環嚮應力和徑嚮應變等結構響應時誤差也較小。3種構型的計算結果與有限元計算結果的比值變化趨勢基本相同,其中三角形和Kagome構型的計算結果較正方形構型的計算結果較為準確。通過對所得結果進行分析,可以髮現該高階位移場理論在計算圓柱殼體結構響應時有效、準確,可以作為預測該類結構響應的計算方法。
기우고계위이장이론연구료간지조건릉경형원주각체재내압력작용하적결구향응。수선,건립승수내압원주각체적평형방정,계산재해재하작용하적각항동성재료적향응,여탄성역학이론해진행대비,험증소득평형방정적정학성。채용균균화방법,장정방형,삼각형화Kagome 3충다공금속원주각체등효위정교각향이성적재료,계산료재내압하적결구향응,병여유한원계산결과진행대비,결과표명문중방법소득결과여유한원적결과비상접근,계산득도적경향위이화축향응변여유한원적계산기본상동,경향응력,배향응력화경향응변등결구향응시오차야교소。3충구형적계산결과여유한원계산결과적비치변화추세기본상동,기중삼각형화Kagome구형적계산결과교정방형구형적계산결과교위준학。통과대소득결과진행분석,가이발현해고계위이장이론재계산원주각체결구향응시유효、준학,가이작위예측해류결구향응적계산방법。
A metallic cylindrical lattice tube under internal pressure was analyzed by using the HODF theory .The response of the structure was obtained and compared with that obtained by using the FEM analysis .By using the homogenization method , three cylindrical lattice tubs , whose lattice types were Triangle , Square, and Kagome re-spectively , under internal pressure were homogenized to be orthotropic material and calculated by HODF theory . The HODF theoretical results and the FEM results were respectively obtained and their comparisons show that the differences are very small .The radial displacement and axial displacement obtained with HODF theory are nearly the same as the respective displacements obtained with FEM .The errors in radial stress , hoop stress and radial strain are relatively small .The ratios of the displacements obtained respectively with HODF theory and FEM are calculated and the patterns of these respective ratios are nearly the same .The results of Triangle and Kagome are better than the results of Square .The comparison and analysis of calculated results confirm preliminarily that the higher-order displacement theory can be used to calculate the correct responses of the metallic cylindrical lattice tube under internal pressure .