环扇形薄板弯曲问题环向辛体系的研究
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摘要
本研究建立了反相高效液相色谱法(RP-HPLC)在鲫血浆及各组织中同时检测氟苯尼考和氟苯尼考胺的方法，并以此方法研究了20℃水温条件下单次口灌氟苯尼考在健康鲫体内的药物动力学特征和多次口灌的残留消除规律。
以乙酸乙酯为萃取剂，取上清液蒸干，残留物用流动相溶解，并用正已烷去脂，下清液取出检测。用Agilent1100型高效液相色谱仪，Varian Microsorb-MV-C_(18)色谱柱(250×4.6mm~2，5μm)，外加保护柱12.5×4.6mm~2；紫外检测器，波长为223nm；柱温35℃；进样量60μL；以乙腈／0.01M乙酸盐缓冲液(25／75 VN)为流动相，用乙酸盐调节pH至3.8；流速1.0mL／min。结果显示，在0.25～32μg／g浓度范围内，线性关系良好；回收率的值：血浆中，氟苯尼考为：96～103％，氟苯尼考胺为：94～104％；肌肉中，氟苯尼考为：100～108％，氟苯尼考胺为：94～108％；肝胰脏中，氟苯尼考为：97～105％，氟苯尼考胺为：97～108％；肾中，氟苯尼考为：97～108％，氟苯尼考胺为：96～109％；皮肤中，氟苯尼考为：97～108％，氟苯尼考胺为：97～110％。氟苯尼考和氟苯尼考胺的检测限分别为：血浆中0.02μg／g，0.010μg／g；肌肉中0.010μg／g，0.005μg／g；肝胰脏中0.020μg／g，0.010μg／g；肾脏中0.060μg／g，0.030μg／g；皮肤中0.020μg／g，0.010μg／g。日内变异系数均小于5％，日间变异系数均小于15％。结果表明，所建立的检测方法具有灵敏、准确、简便的特点，可以同时检测鱼组织中氟苯尼考和氟苯尼考胺的含量。
本实验研究了在20℃水温条件下单次口灌给药后氟苯尼考在鲫体内的药物代谢动力学。所选鲫体重为250±30g，给药剂量为10mg／(kgbw).d。结果显示，20℃水温条件下药-时曲线符合有吸收一室模型，主要药物动力学参数为：吸收速率常数K_a为0.75h~(-1)；消除半衰期t_(1／2ke)。为10.69h；药时曲线下面积AUC为53.74μg·mL~(-1)·h；表观分布容积V_d／F为2.87 L／kg；清除率CL_b为0.19 L·h~(-1)·kg~(-1)；达峰时间T_p为3.59h；峰浓度C_(max)为2.76μg／mL。以10mg／(kgbw).d的剂量连续3次口灌给药后，于最后一次给药后的第2、7、9、13、18h和1、2、3、5、7、10、15d采集各组织样品，研究该药物在鲫体内的药物消除及残留规律。结果显示，氟苯尼考的消除速率比其代谢物氟苯尼考胺快，所有个体带皮肌肉中氟苯尼考的浓度在2d时已在1μg／g以下，在5d后已不能检测到药物。氟苯尼考胺的平均浓度在3d时才降至1μg／g以下，而个别个体中还高于此浓度，10d后仍能检测到药物，15d后不能再检测到药物。给药3d后在鲫的可食组织中氟苯尼考和氟苯尼考胺两者之和的平均总浓度高于1μg／g，在给药5d后实验所测每个个体中氟苯尼考和氟苯尼考胺两者的总浓度均低于1μg／g，7d后仅能检测到氟苯尼考胺，15d后二者均检测不到。
通过药物动力学实验得知，以10mg／(kgbw).d的剂量口灌给药后1d内的药物浓度在MIC以上；通过药物残留实验得知，为确保所有个体可食组织中含药量均低于低于欧盟和中国的MRLs，建议在20℃水温条件下休药期不少于5d。
In classical elasticity mechanics, the solution method is to eliminate the some ofunknown variables and can get simplest equation in a brief form. As the result, the rank ofequation is increased, so separating the variables and expanding eigenfunction methodscannot be applied to solve the equation.
In this paper, systematic theory is applied to the mechanics of elasticity. There is analogyrelationship between plane elasticity and plate bending. Their governing equations are bothbiharmonic equation. Strain-displacement relation, stress function-stress relationship andstress-strain relationship in plane elasticity correspond to bending moment-bending momentfunction, deflection-curvature relationship and bending moment- curvature relationship inplate bending respectively. So the symplectic solution system can be applied in plate bendingas plane elasticity. Dual equations and Hamiltonian operator matrix can be derived from thePro-H-R variational principle, and it becomes the transverse eigen problem of Hamiltonianmatrix after separation of variable. There is the adjoint symplectic orthogonality relationshipbetween the eigenfunction vectors, so any solution can be expanded by the eigenfunctionvectors. In this paper, the general form of non-zero eigenfunction vector can be given, andthen be substituted into lateral boundary conditions to get the transcendental equation fornon-zero eigenvalues. So the non-zero eigenvalues and eigenvectors can be presented.According to the adjoint symplectic orthogonality relationship and the expansion theorem, theexpression which satisfies all control equation in the domain and two lateral boundaryconditions is listed. After substituting it into two end boundary conditions, solution of theoriginal problem is obtained.
In this paper, several examples are given, and excellent accuracy has been obtainare byusing only several eigenvalues. The new method presents the analytical solutions in annularsector plate via separation of variables and expansion of eigenfunction vector. It breaks thelimitation of traditional semi-inverse solution. The results show that the new method has vastapplication foreground.
以乙酸乙酯为萃取剂，取上清液蒸干，残留物用流动相溶解，并用正已烷去脂，下清液取出检测。用Agilent1100型高效液相色谱仪，Varian Microsorb-MV-C_(18)色谱柱(250×4.6mm~2，5μm)，外加保护柱12.5×4.6mm~2；紫外检测器，波长为223nm；柱温35℃；进样量60μL；以乙腈／0.01M乙酸盐缓冲液(25／75 VN)为流动相，用乙酸盐调节pH至3.8；流速1.0mL／min。结果显示，在0.25～32μg／g浓度范围内，线性关系良好；回收率的值：血浆中，氟苯尼考为：96～103％，氟苯尼考胺为：94～104％；肌肉中，氟苯尼考为：100～108％，氟苯尼考胺为：94～108％；肝胰脏中，氟苯尼考为：97～105％，氟苯尼考胺为：97～108％；肾中，氟苯尼考为：97～108％，氟苯尼考胺为：96～109％；皮肤中，氟苯尼考为：97～108％，氟苯尼考胺为：97～110％。氟苯尼考和氟苯尼考胺的检测限分别为：血浆中0.02μg／g，0.010μg／g；肌肉中0.010μg／g，0.005μg／g；肝胰脏中0.020μg／g，0.010μg／g；肾脏中0.060μg／g，0.030μg／g；皮肤中0.020μg／g，0.010μg／g。日内变异系数均小于5％，日间变异系数均小于15％。结果表明，所建立的检测方法具有灵敏、准确、简便的特点，可以同时检测鱼组织中氟苯尼考和氟苯尼考胺的含量。
本实验研究了在20℃水温条件下单次口灌给药后氟苯尼考在鲫体内的药物代谢动力学。所选鲫体重为250±30g，给药剂量为10mg／(kgbw).d。结果显示，20℃水温条件下药-时曲线符合有吸收一室模型，主要药物动力学参数为：吸收速率常数K_a为0.75h~(-1)；消除半衰期t_(1／2ke)。为10.69h；药时曲线下面积AUC为53.74μg·mL~(-1)·h；表观分布容积V_d／F为2.87 L／kg；清除率CL_b为0.19 L·h~(-1)·kg~(-1)；达峰时间T_p为3.59h；峰浓度C_(max)为2.76μg／mL。以10mg／(kgbw).d的剂量连续3次口灌给药后，于最后一次给药后的第2、7、9、13、18h和1、2、3、5、7、10、15d采集各组织样品，研究该药物在鲫体内的药物消除及残留规律。结果显示，氟苯尼考的消除速率比其代谢物氟苯尼考胺快，所有个体带皮肌肉中氟苯尼考的浓度在2d时已在1μg／g以下，在5d后已不能检测到药物。氟苯尼考胺的平均浓度在3d时才降至1μg／g以下，而个别个体中还高于此浓度，10d后仍能检测到药物，15d后不能再检测到药物。给药3d后在鲫的可食组织中氟苯尼考和氟苯尼考胺两者之和的平均总浓度高于1μg／g，在给药5d后实验所测每个个体中氟苯尼考和氟苯尼考胺两者的总浓度均低于1μg／g，7d后仅能检测到氟苯尼考胺，15d后二者均检测不到。
通过药物动力学实验得知，以10mg／(kgbw).d的剂量口灌给药后1d内的药物浓度在MIC以上；通过药物残留实验得知，为确保所有个体可食组织中含药量均低于低于欧盟和中国的MRLs，建议在20℃水温条件下休药期不少于5d。
In classical elasticity mechanics, the solution method is to eliminate the some ofunknown variables and can get simplest equation in a brief form. As the result, the rank ofequation is increased, so separating the variables and expanding eigenfunction methodscannot be applied to solve the equation.
In this paper, systematic theory is applied to the mechanics of elasticity. There is analogyrelationship between plane elasticity and plate bending. Their governing equations are bothbiharmonic equation. Strain-displacement relation, stress function-stress relationship andstress-strain relationship in plane elasticity correspond to bending moment-bending momentfunction, deflection-curvature relationship and bending moment- curvature relationship inplate bending respectively. So the symplectic solution system can be applied in plate bendingas plane elasticity. Dual equations and Hamiltonian operator matrix can be derived from thePro-H-R variational principle, and it becomes the transverse eigen problem of Hamiltonianmatrix after separation of variable. There is the adjoint symplectic orthogonality relationshipbetween the eigenfunction vectors, so any solution can be expanded by the eigenfunctionvectors. In this paper, the general form of non-zero eigenfunction vector can be given, andthen be substituted into lateral boundary conditions to get the transcendental equation fornon-zero eigenvalues. So the non-zero eigenvalues and eigenvectors can be presented.According to the adjoint symplectic orthogonality relationship and the expansion theorem, theexpression which satisfies all control equation in the domain and two lateral boundaryconditions is listed. After substituting it into two end boundary conditions, solution of theoriginal problem is obtained.
In this paper, several examples are given, and excellent accuracy has been obtainare byusing only several eigenvalues. The new method presents the analytical solutions in annularsector plate via separation of variables and expansion of eigenfunction vector. It breaks thelimitation of traditional semi-inverse solution. The results show that the new method has vastapplication foreground.
引文
[1] Timoshenko S P, Woinowsky-Krieger S. Theory of plates and shells. New York: McGraw-Hill, 1959
[2] 钟万勰著．弹性力学求解新体系．大连：大连理工大学出版社，1995
[3] 姚伟岸，钟万勰著．辛弹性力学．北京：高等教育出版社，2002
[4] 王龙甫编．弹性理论．北京：科学出版社，1984
[5] 吴家龙编著．弹性力学．上海：同济大学出版社，1993
[6] 陆明万，罗学富．弹性理论基础．清华大学出版社，2001
[7] 徐芝纶．弹性力学．北京：高等教育出版社，1990
[8] Madhujit Mukhopadhyay. A Semianalytic Solution for radially supported curved plates in bending. Forsch.Ing.-Wes.44 (1978) Nr.6
[9] 钱民刚，严宗达．扇形板的富里哀-贝塞尔级数解．应用数学和力学，1985，6(4)
[10] 钱民刚，严宗达．环形板的Fourier-Bessel级数解．北京建筑工程学院学报，1990
[11] 钱民刚，严宗达．沿直边简支的环扇形板的Fourier-Bessel级数解．北京建筑工程学院学报，1995．
[12] 钱民刚，严宗达．沿直边非简支的环扇形板的Fourier-Bessel级数解-扇形、环形、环扇形板的一般解．北京建筑工程学院学报，1996
[13] Sternberg E and Koiter W T. The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity. J Applied Mechanics,1958,25(3):575-581
[14] Muschelishvili N I.Some basic problems of the mathematical theory of elasticity. Groningen: Noordholf, 1953
[15] Southwell R V.On the analogues relating flexure and extension of flat plate. Quarterly Journal of Mechanics and Mathematics, 1950(3):257
[16] Fraeijs De Veubeke B, Zienkiewicz O C. Strain-energy bounds of finite-element analysis by slab analogy. J Strai Analysis, 1967(2):265-271
[17] Fraeijs De Veubeke B, Sander G.An equilibrium model for plate bending. I J Solids & Structures, 1968, 4(4):447-468
[18] 姚伟岸．极坐标哈密顿体系约当型与弹性楔的佯谬解．力学学报．2001，33(1)：79-86
[19] 钟万勰，徐新生，张洪武．弹性曲梁问题的直接法．工程力学，1996，13(4)：1-8
[20] 胡海昌著．弹性力学的变分原理及其应用．北京：科学出版社，1981
[21] 钟万勰，姚伟岸．板弯曲求解新体系及其应用．力学学报，1999，31(2)：173-184
[22] 钟万勰，姚伟岸．板弯曲与平面弹性有限元的同一性．计算力学学报，1998，15(1)：1-13
[23] 钟万勰，姚伟岸．板弯曲与平面弹性问题的多类变量变分原理．力学学报，1999，31(6)：717-723
[24] 钟万勰，姚伟岸．板弯曲求解新体系—力法哈密顿体系及其应用．上海：上海大学出版社，1997，121-129
[25] 钟万勰．互等定理与共轭辛正交关系．力学学报，1992，24(4)：432-437
[26] 钟万勰．条形域弹性平面问题与哈密顿体系．计算结构力学及其应用，1990，8(3)：373-384
[27] 钟万勰．弹性平面扇形域问题及哈密顿体系．应用数学和力学，1994，15(12)：1057-1066
[28] 苏滨，哈密顿体系在各向异性板弯曲问题中的应用．[硕士学位论文]．大连：大连理工大学工程力学系，2000
[29] Yao Weian, Zhong Wanxie, Su Bin.New solution system for circular sector plate bending and its application. Acta Mechanica Solida Sinica,1999,12(4):307-315
[30] Zhong Wanxie and Yang Zaishi.Partial differential equations and Hamiltonian system. In: Cheng FY, Fu Zizhi, eds. Computational Mechanics in Structural Engineering. London: Elsevier, 1992 32-48
[31] Zhong Wanxie and Williams F W.On the localization of the vibration mode of sub-structural chain-type structure. Proc Instn Mech Engrs Part C, 1991,205(C4) :281-288
[30] Whittaker E T. A treatise on the analytical dynamics.4th ed. Cambridge: Cambridge Univ Press,1960
[33] Arnold Ⅵ. Mathematical methods of classical mechanics. New York: Springer-Verlag, 1978
[34] 龙云亮，文希理，谢处方．复平面上超越函数零点的数值计算[J]，数值计算与计算机应用，1994，2：88-92
[2] 钟万勰著．弹性力学求解新体系．大连：大连理工大学出版社，1995
[3] 姚伟岸，钟万勰著．辛弹性力学．北京：高等教育出版社，2002
[4] 王龙甫编．弹性理论．北京：科学出版社，1984
[5] 吴家龙编著．弹性力学．上海：同济大学出版社，1993
[6] 陆明万，罗学富．弹性理论基础．清华大学出版社，2001
[7] 徐芝纶．弹性力学．北京：高等教育出版社，1990
[8] Madhujit Mukhopadhyay. A Semianalytic Solution for radially supported curved plates in bending. Forsch.Ing.-Wes.44 (1978) Nr.6
[9] 钱民刚，严宗达．扇形板的富里哀-贝塞尔级数解．应用数学和力学，1985，6(4)
[10] 钱民刚，严宗达．环形板的Fourier-Bessel级数解．北京建筑工程学院学报，1990
[11] 钱民刚，严宗达．沿直边简支的环扇形板的Fourier-Bessel级数解．北京建筑工程学院学报，1995．
[12] 钱民刚，严宗达．沿直边非简支的环扇形板的Fourier-Bessel级数解-扇形、环形、环扇形板的一般解．北京建筑工程学院学报，1996
[13] Sternberg E and Koiter W T. The wedge under a concentrated couple: a paradox in the two-dimensional theory of elasticity. J Applied Mechanics,1958,25(3):575-581
[14] Muschelishvili N I.Some basic problems of the mathematical theory of elasticity. Groningen: Noordholf, 1953
[15] Southwell R V.On the analogues relating flexure and extension of flat plate. Quarterly Journal of Mechanics and Mathematics, 1950(3):257
[16] Fraeijs De Veubeke B, Zienkiewicz O C. Strain-energy bounds of finite-element analysis by slab analogy. J Strai Analysis, 1967(2):265-271
[17] Fraeijs De Veubeke B, Sander G.An equilibrium model for plate bending. I J Solids & Structures, 1968, 4(4):447-468
[18] 姚伟岸．极坐标哈密顿体系约当型与弹性楔的佯谬解．力学学报．2001，33(1)：79-86
[19] 钟万勰，徐新生，张洪武．弹性曲梁问题的直接法．工程力学，1996，13(4)：1-8
[20] 胡海昌著．弹性力学的变分原理及其应用．北京：科学出版社，1981
[21] 钟万勰，姚伟岸．板弯曲求解新体系及其应用．力学学报，1999，31(2)：173-184
[22] 钟万勰，姚伟岸．板弯曲与平面弹性有限元的同一性．计算力学学报，1998，15(1)：1-13
[23] 钟万勰，姚伟岸．板弯曲与平面弹性问题的多类变量变分原理．力学学报，1999，31(6)：717-723
[24] 钟万勰，姚伟岸．板弯曲求解新体系—力法哈密顿体系及其应用．上海：上海大学出版社，1997，121-129
[25] 钟万勰．互等定理与共轭辛正交关系．力学学报，1992，24(4)：432-437
[26] 钟万勰．条形域弹性平面问题与哈密顿体系．计算结构力学及其应用，1990，8(3)：373-384
[27] 钟万勰．弹性平面扇形域问题及哈密顿体系．应用数学和力学，1994，15(12)：1057-1066
[28] 苏滨，哈密顿体系在各向异性板弯曲问题中的应用．[硕士学位论文]．大连：大连理工大学工程力学系，2000
[29] Yao Weian, Zhong Wanxie, Su Bin.New solution system for circular sector plate bending and its application. Acta Mechanica Solida Sinica,1999,12(4):307-315
[30] Zhong Wanxie and Yang Zaishi.Partial differential equations and Hamiltonian system. In: Cheng FY, Fu Zizhi, eds. Computational Mechanics in Structural Engineering. London: Elsevier, 1992 32-48
[31] Zhong Wanxie and Williams F W.On the localization of the vibration mode of sub-structural chain-type structure. Proc Instn Mech Engrs Part C, 1991,205(C4) :281-288
[30] Whittaker E T. A treatise on the analytical dynamics.4th ed. Cambridge: Cambridge Univ Press,1960
[33] Arnold Ⅵ. Mathematical methods of classical mechanics. New York: Springer-Verlag, 1978
[34] 龙云亮，文希理，谢处方．复平面上超越函数零点的数值计算[J]，数值计算与计算机应用，1994，2：88-92