CN106547994A - A kind of composite blade plate Optimization Design based on Laminated Plate Theory - Google Patents

Abstract

The invention discloses a kind of composite blade plate Optimization Design based on Laminated Plate Theory，The material for specifically including selection composite blade plate carries out preliminary structure design and to laminate laying quantity to which、Laying order and laying direction etc. are optimized design，Code solution axial rigidity is write based on Analysis of Symmetric Laminated Plates theory to meeting construction of condition、Bending stiffness and torsional rigidity，Structure is simultaneously divided some interval computation stiffness coefficient values by Rational choice bend stiffness，The structure of some maximum rigidity coefficients is retained and is applied in union of fracture phantom carries out finite element analyses，Select the design of optimum，The present invention carries out stress shielding phenomenon when comprehensive optimization design ingenious utilization fracture fixation to composite blade plate，Reduce axial rigidity and maximize bending and the torsional rigidity of blade plate，Reduce adverse effect of the stress shielding to union of fracture.

Description

A kind of composite blade plate Optimization Design based on Laminated Plate Theory

Technical field

The invention belongs to the optimisation technique field of composite holder, and in particular to a kind of answering based on Laminated Plate Theory Condensation material blade plate Optimization Design.

Background technology

It is one of conventional means of orthopaedics therapy fracture that interior fixation is carried out using blade plate.Blade plate is used to fracture site After fixation, the mobility of fracture end depends on the size of external load, the tissue bridged between the rigidity of fixed system and fracture Rigidity.Traditional blade plate mostly is metal material, has the following disadvantages：

(1) elastic modelling quantity is excessive with bone difference, has stress-shielding effect.

(2) its corrosion-resistant, fatigue resistance is poor, be susceptible to failure.

(3) big with the bone contact area, blood supply of destruction cortical bone.

(4) cause malunion of fracture, bone does not connect, the refracture phenomenon after fracture, be unfavorable for union of fracture.

(5) with tissue compatibility Shortcomings.

(6) not with the physical and mechanical propertiess being adapted with natural fabric.

Therefore it is badly in need of solving during union of fracture the problems such as the stress-shielding effect of fracture fixing apparatuss.

Augat et al. discoveries, the rigidity of reduction fixed plate, the load level of increase fracture site that can be favourable and stimulation The reconstruction of callus tissue, but the factor for being unfavorable for broken ends of fractured bone fine motion that increases (such as shearing and torsion) may be also resulted in so as to destroy The stability of fracture site.Therefore selection is adapted to tissue characteristic and the less holder material type of rigidity also becomes anxious The problem that need to be solved.

The content of the invention

The invention provides a kind of composite blade plate Optimization Design based on Laminated Plate Theory, using fixation During device treatment fracture, stress shielding phenomenon is inevitable, the present invention according to laminate design principle to laminate laying total quantity, Laminate gross thickness, laying quantity, the thickness of laying, laying order and laying direction are optimized design, dexterously dissolve The unfavorable factor that stress shielding phenomenon is brought for fracture healing process so as to while axial flexibility is kept, maximum limit The bending of the raising blade plate of degree and torsional rigidity, so as to reduce axial rigidity, reduce stress shielding phenomenon to union of fracture The adverse effect for causing, promotes the healing of fracture.

A kind of composite blade plate Optimization Design based on Laminated Plate Theory comprises the steps：

Step one：The material for choosing composite blade plate carries out preliminary structure design to which；

Step 2：The structural nature of composite blade plate is laminated plate structure, and the optimization design is first according to reality Human fracture position carries out appropriate design to blade plate gross thickness, then according to laminate design principle to laminate laying sum The quantity of the quantity and flax fiber and/or epoxide resin material laying of amount, carbon fiber and/or epoxide resin material laying, paving Layer thickness, laying order and laying direction be optimized design, the laminate design principle is as follows：

1) balance and symmetry principle of paving：

Composite blade plate structure is designed to into Analysis of Symmetric Laminated Plates form, and laminate laying order must be with regard to lamination Plate midplane is symmetrical；To avoid in production process due to temperature change and drawing-cut, the buckling deformation that stretching-bending coupling is caused, most The bending strength of bigization laminate；

2) laying orientation principle：

Laying direction θ in laminate, is the laying with respect to reference axis for θ ° of direction, and scope is+θ ° and-θ ° from 0 ° to 90 ° Laying quantity is identical, and the angle between adjacent laying is less than 45 °, and the laying quantitative proportion in any laying direction is less than 60%, with Maximize the bending strength of laminate；

3) laying minimum scale principle：

To make the matrix of composite stand under load and not avoid thermal expansion system too high in manufacture process in all directions Number causes buckling deformation, and the laying minimum scale in its 0 °, 90 ° laying direction of laminate of laying composition is 10%；

4) open region laying principle：

Angle≤45 ° of adjacent laying should be made in structural openings area, to reduce inter-laminar stress；Opening shape should be adopted as far as possible With circular hole, because circle hole-edge stress concentration is less；In addition in opening, the fiber of cut-out should lack as far as possible；

5) lay principle of temporal sequence：

Mainly from from the aspect of three：Each orientation monolayer should be made to be uniformly distributed along lamination plate thickness as far as possible, it is to avoid by same paving The laying at layer angle is concentrated and is placed；If have to use, 4 layers are usually no more than, to reduce cracking and the side of two kinds of oriented layers Fate layer；If containing ± 45 ° of layers, 0 ° of layer and 90 ° of layers in laminate, should try one's best between+45 ° of layers and -45 ° of layers with 0 ° of layer or 90 ° of layers separate, and are separated with+45 ° of layers or -45 ° of layers between 0 ° of layer and 90 ° of layers, and should avoid laying 90 ° of layers in groups, to drop Low inter-laminar stress；For exposure laminate outside, fabric or ± 45 ° of layers are laid on surface, will be with preferable working service Property, it is also possible to improve laminate and compression and shock resistance；In addition, laying order is affected on laminate stability bearing capacity Very big, this factor should also take into full account；

6) face principle of paving in laminate：

Middle face refers to the plane of symmetry in the middle of Analysis of Symmetric Laminated Plates, and there is the laying that at least 6 laying directions are 90 ° in middle face； Minimum degree affects to increase its lateral stiffness while bending and torsional rigidity；

7) thickness design principle：

In structure Varying-thickness region, laying number increasing or decreasing should form step and gradually change, because the mutation meeting of thickness Cause stress concentration；It is required that each step width is close and >=60 °, shoulder height less than width 1/10；Then on surface Continuous coating is laid, to prevent from stripping damage outside step；

Step 3：The structure of laminate design principle is unsatisfactory in removing be possible to structure；

Step 4：Theory of the structure based on Analysis of Symmetric Laminated Plates to meeting laminate design principle, with C language in VS2013 Code is write under platform, its axial rigidity, bending stiffness and torsional rigidity is solved respectively；

A. the calculating of axial rigidity：

In formula, axial rigidities of the EA for blade plate, width of the b for blade plate；

B. the calculating of bending stiffness：

In formula, EI_yyFor the bending stiffness of blade plate；

C. the calculating of torsional rigidity：

In formula, torsional rigidities of the GJ for blade plate；

Regard blade plate as compound girder construction and process is analyzed based on classical Laminated Plate Theory, it is axial rigidity, curved The derivation of stiffness and torsional rigidity is as follows：

The power and torque such as formula (4) of laminate unit length, (5) are shown：

In formula, A is tensible rigidity matrix, B is Coupling stiffness matrix, D is bending stiffness matrix, because B_ij=0, thus power and Shown in torque matrix such as formula (6), formula (7)：

In formula,For the axial force of laminate, width of the b for laminate, using Laminated Plate Theory, N_xFor list in laminate The power of bit length, solution formula is as shown in (8)；

It is assumed that N_xFor (the namely N in formula (6) of unique power in laminate_y=N_xy=0), formula (6) is changed into：

In formula,For matrix [A]^-1In element,For the strain on x-axis direction；

In formula, u₀For the displacement on x-axis direction, in narrower girder construction, when length-width ratio is sufficiently high, it can be assumed that u₀=u₀(x), therefore formula (11) can be equal to equation below (13)：

Anisotropy Symmetric Beam is obtained according to the axial strain (i.e. formula (13)) of formula (12) and isotropism beam The computing formula (as shown in formula (14)) of axial rigidity：

In order to be bent rigidity EI_yy, a Based on Pure Bending Moment (M_y) act on X-Z plane, the torque of unit lengthMeter Calculate shown in formula such as formula (15)：

In formula,For matrix [D]^-1In element；

The computing formula such as formula (18) of the planar curvature outside the planar curvature of X-Z plane and middle face, (19) are shown：

In formula, w0 is the displacement on combination beam z-axis direction, because beam is narrower, here it is assumed that w0=w0 (x), formula (18) It is equal to formula (20)；

According to formula (20) and the curvature (d of isotropic rectangle beam²w/dx²=-(M/EI)), then anisotropy rectangular beam Bending stiffness such as formula (21) shown in：

To obtain the torsional rigidity of composite blade plate square-section, it is assumed that any torque T being applied on beam can be produced Raw unit length moment of torsion (M_xy) and subsequent shear flow (q), shown in the shear flow that torque T causes such as formula (22)：

T=2qh ' b ' (22)

In formula, h ' is the thickness of laminate after shear flow effect, and b ' is the width of laminate after shear flow effect；

The moment of torsion of square-section unit length is：

M_xy=-qh ' (23)

Can be obtained by formula (22), (23)：

T=-2bM_xy (24)

By formula (7), it is contemplated that actually there is no curvature K of axial force and Moment on beam, in laminate outside face_xy For：

Shown in the torsion ψ and torsion curvature ξ such as formula (27), (28) of beam middle section：

Curvature outside face in composite beam can be expressed as by formula (19) and (27)：

Therefore can obtain：

By formula (24), (26), (30), torsion curvature such as formula of the rectangle composite beam in the torque for being applied can be obtained (32) shown in：

According to the computing formula (33) of formula (31) and the torsion curvature of isotropism beam, with square-section and sufficiently high Flakiness ratio be symmetrical composite beam torsional rigidity such as formula (33) shown in：

ξ=T/GJ (32)

Step 5：According to the result of calculation of step 4, structure of the bending stiffness less than setting is removed；

Step 6：Suitable interval is selected according to its bending stiffness to meeting all structures of laminate design principle, by which It is divided into some intervals；

Step 7：The structured stiffness coefficient of institute in each described interval is calculated respectively, retains stiffness coefficient in each interval A kind of structure of value highest；

The computing formula of stiffness coefficient is as follows：

In formula, SEF_iFor the stiffness coefficient of different structure blade plate, EA_minFor the minima of axial rigidity, EA_iFor different knots The axial rigidity of structure blade plate, GJ_iFor the torsional rigidity of different structure blade plate, GJ_maxFor the maximum of torsional rigidity；

Step 8：The structure of reservation is applied in union of fracture phantom carries out finite element analyses, selects optimum Blade plate structure, completes the optimization design of blade plate；

The blade plate structure of reservation is applied in the union of fracture analogue system of C language written in code, finite element is carried out Analysis, takes into full account the actual therapeutic scheme of patient, simulates different gait load when writing code, and will be using composite The fracture healing process of the fracture model after plate fixation is divided into Post operation when plate fixation (i.e. just use), solid immediately (about 4-6 is all) and union of fracture stage after fixed a period of time, respectively the fracture model is carried out in the different stages limited Meta-analysis, obtain parameter as follows：Axially-movable, shearing motion, compressive stress, contact moment of flexure, mean stress and maximum distortion；According to The different composite blade plate structures are analyzed, are finally selected most beneficial for union of fracture by the result of the parameter The composite blade plate optimum optimization structure.

The invention has the beneficial effects as follows：In fracture healing process, the stress shielding phenomenon of fracture fixing apparatuss is inevitable, this Invention have selected carbon fiber and/or epoxy resin and fiber and/or epoxy resin as the composite wood of composite blade plate Material, its density are little, and specific strength and specific modulus are high, and weight mitigates significantly and fatigue strength is high, and fail-safety is good, have before its fracture Obvious omen, therefore solve the problems, such as that traditional metal materials blade plate, by the sudden destruction of no omen under load, reduces which The injury produced to human body is damaged, its damping and good corrosion resistance, little to injury of human in addition；Present invention discover that stress shielding Always not unfavorable to union of fracture, rigidity value when cleverly utilizing and improve stress shielding even can promote union of fracture, It is rational choose bending stiffness, torsional rigidity, can part opposing compressive stress, so as to stimulate reinventing for fracture callus, therefore root According to laminate design principle to laminate laying total quantity, laminate gross thickness, carbon fiber and/or epoxide resin material laying The quantity of quantity and flax fiber and/or epoxide resin material laying, the thickness of laying, laying order and laying direction are carried out Optimization design, fracture fixing apparatuss by the comprehensive optimization to composite blade plate structure and when cleverly having used union of fracture The stress shielding phenomenon brought, makes blade plate while its axial flexibility is kept, improves the curved of blade plate to greatest extent Bent and torsional rigidity, so as to reduce axial rigidity, solves the excessive, stress shielding of rigidity that traditional blade plate brings etc. unfavorable In the problem of union of fracture, to greatest extent using the performance of material, the rigidity of fixation of optimum human fracture healing is obtained, from And the factor for being unfavorable for union of fracture is reduced, promote union of fracture.

Description of the drawings

Fig. 1 is the schematic flow sheet of composite blade plate optimization.

Fig. 2 a are the rectangle Laminated Beams by axial load and moment of flexure, and b is the shear flow of torque T and gained.

Specific embodiment

In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and specific embodiment to the present invention composite Blade plate Optimization Design is described in detail.

As shown in figure 1, a kind of composite blade plate Optimization Design based on Laminated Plate Theory comprises the steps：

Step one：Carry out structure optimization to composite blade plate, composite blade plate cladding material be carbon fiber and/ Or epoxy resin inner layer material is flax fiber and/or epoxy resin；

Step 2：The structural nature of composite blade plate is laminated plate structure, and the optimization design is first according to reality Human fracture position carries out appropriate design to blade plate gross thickness, then according to laminate design principle to laminate laying sum The quantity of the quantity and flax fiber and/or epoxide resin material laying of amount, carbon fiber and/or epoxide resin material laying, paving Layer thickness, laying order and laying direction be optimized design, the laminate design principle is as follows：

1) balance and symmetry principle of paving：

Composite blade plate structure is designed to into Analysis of Symmetric Laminated Plates form, and laminate laying order must be with regard to lamination Plate midplane is symmetrical；To avoid in production process due to temperature change and drawing-cut, the buckling deformation that stretching-bending coupling is caused, most The bending strength of bigization laminate；

2) laying orientation principle：

Laying direction θ in laminate, is the laying with respect to reference axis for θ ° of direction, and scope is+θ ° and-θ ° from 0 ° to 90 ° Laying quantity is identical, and the angle between adjacent laying is less than 45 °, and the laying quantitative proportion in any laying direction is less than 60%, with Maximize the bending strength of laminate；

3) laying minimum scale principle：

To make the matrix of composite stand under load and not avoid thermal expansion system too high in manufacture process in all directions Number causes buckling deformation, and the laying minimum scale in its 0 °, 90 ° laying direction of laminate of laying composition is 10%；

4) open region laying principle：

Angle≤45 ° of adjacent laying should be made in structural openings area, to reduce inter-laminar stress；Opening shape should be adopted as far as possible With circular hole, because circle hole-edge stress concentration is less；In addition in opening, the fiber of cut-out should lack as far as possible；

5) lay principle of temporal sequence：

Mainly from from the aspect of three：Each orientation monolayer should be made to be uniformly distributed along lamination plate thickness as far as possible, it is to avoid by same paving The laying at layer angle is concentrated and is placed；If have to use, 4 layers are usually no more than, to reduce cracking and the side of two kinds of oriented layers Fate layer；If containing ± 45 ° of layers, 0 ° of layer and 90 ° of layers in laminate, should try one's best between+45 ° of layers and -45 ° of layers with 0 ° of layer or 90 ° of layers separate, and are separated with+45 ° of layers or -45 ° of layers between 0 ° of layer and 90 ° of layers, and should avoid laying 90 ° of layers in groups, to drop Low inter-laminar stress；For exposure laminate outside, fabric or ± 45 ° of layers are laid on surface, will be with preferable working service Property, it is also possible to improve laminate and compression and shock resistance；In addition, laying order is affected on laminate stability bearing capacity Very big, this factor should also take into full account；

6) face principle of paving in laminate：

Middle face refers to the plane of symmetry in the middle of Analysis of Symmetric Laminated Plates, and there is the laying that at least 6 laying directions are 90 ° in middle face； Minimum degree affects to increase its lateral stiffness while bending and torsional rigidity；

7) thickness design principle：

In structure Varying-thickness region, laying number increasing or decreasing should form step and gradually change, because the mutation meeting of thickness Cause stress concentration；It is required that each step width is close and >=60 °, shoulder height less than width 1/10；Then on surface Continuous coating is laid, to prevent from stripping damage outside step；

Step 3：The structure of laminate design principle is unsatisfactory in removing be possible to structure；

Step 4：For theory of the structure based on Analysis of Symmetric Laminated Plates for meeting laminate design principle, existed with C language Code is write under VS2013 platforms, its axial rigidity, bending stiffness and torsional rigidity is solved respectively；

A. the calculating of axial rigidity：

In formula, axial rigidities of the EA for blade plate, width of the b for blade plate；

B. the calculating of bending stiffness：

In formula, EI_yyFor the bending stiffness of blade plate；

C. the calculating of torsional rigidity：

In formula, torsional rigidities of the GJ for blade plate；

Regard blade plate as compound girder construction and analyze Laminated Plate Theory of the process based on classics, its axial rigidity, The derivation of bending stiffness and torsional rigidity is as follows：

The power and torque such as formula (4) of laminate unit length, (5) are shown：

In formula, A is tensible rigidity matrix, B is Coupling stiffness matrix, D is bending stiffness matrix, because B_ij=0, thus power and Shown in torque matrix such as formula (6), formula (7)：

In formula,For the axial force of laminate, width (as shown in Figure 2 a) of the b for laminate, using Laminated Plate Theory, N_x For the power of unit length in laminate, solution formula is as shown in (8)；

It is assumed that N_xFor (the namely N in formula (6) of unique power in laminate_y=N_xy=0), formula (6) is changed into：

In formula,For matrix [A]^-1In element,For the strain on x-axis direction；

In formula, u₀For the displacement on x-axis direction, in narrower girder construction, when length-width ratio is sufficiently high, it can be assumed that u₀=u₀(x), therefore formula (11) can be equal to equation below (13)：

Anisotropy is obtained according to the axial strain (i.e. shown in formula (13)) of formula (12) and isotropism beam symmetrical Shown in the computing formula of the axial rigidity of beam such as formula (14)：

In order to be bent rigidity EI_yy, a Based on Pure Bending Moment (M_y) act on X-Z plane, as shown in Figure 1a, unit length TorqueShown in computing formula such as formula (15)：

In formula,For matrix [D]^-1In element；

The computing formula such as formula (18) of the planar curvature outside the planar curvature of X-Z plane and middle face, (19) are shown：

In formula, w0 is the displacement on combination beam z-axis direction, because beam is narrower, here it is assumed that w0=w0 (x), formula (18) It is equal to formula (20)；

According to formula (20) and the curvature (d of isotropic rectangle beam²w/dx²=-(M/EI)), then anisotropy rectangular beam Bending stiffness such as formula (21) shown in：

To obtain the torsional rigidity of composite blade plate square-section, it is assumed that any torque T being applied on beam can be produced Raw unit length moment of torsion (M_xy) and subsequent shear flow (q), shear flow (as shown in Figure 2 b) such as formula that torque T causes (22) shown in：

T=2qh ' b ' (22)

In formula, h ' is the thickness of laminate after shear flow effect, and b ' is the width of laminate after shear flow effect；

The moment of torsion of square-section unit length is：

M_xy=-qh ' (23)

Can be obtained by formula (22), (23)：

T=-2bM_xy (24)

By formula (7), it is contemplated that actually there is no curvature K of axial force and Moment on beam, in laminate outside face_xy For：

Shown in the torsion ψ and torsion curvature ξ such as formula (27), (28) of beam middle section：

Curvature outside face in composite beam can be expressed as by formula (19) and (27)：

Therefore can obtain：

By formula (24), (26), (30), torsion curvature such as formula of the rectangle composite beam in the torque for being applied can be obtained (32) shown in：

According to the computing formula (33) of formula (31) and the torsion curvature of isotropism beam, with square-section and sufficiently high Flakiness ratio it is shown for the torsional rigidity such as formula (33) of Symmetric Composite beam：

ξ=T/GJ (32)

Step 5：According to the result of calculation of step 4, remove bending stiffness and be less than setting structure；

Step 6：To meeting all structures of laminate design principle, between according to obtained by calculating, bend stiffness is chosen properly Every being divided into some intervals；

Step 7：The structured stiffness coefficient of institute in each described interval is calculated respectively, retains stiffness coefficient in each interval A kind of structure of value highest；

The computing formula of stiffness coefficient is as follows：

In formula, SEF_iFor the stiffness coefficient of different structure blade plate, EA_minFor the minima of axial rigidity, EA_iFor different knots The axial rigidity of structure blade plate, GJ_iFor the torsional rigidity of different structure blade plate, GJ_maxFor the maximum of torsional rigidity.

Step 8：The structure of reservation is applied in union of fracture phantom carries out finite element analyses, selects optimum Blade plate structure, completes the optimization design of blade plate；

The blade plate structure of reservation is applied in the union of fracture analogue system of C language written in code, finite element is carried out Analysis, takes into full account the actual therapeutic scheme of patient, simulates different gait load when writing code, and will be using composite The fracture healing process of the fracture model after plate fixation is divided into Post operation when plate fixation (i.e. just use), solid immediately (about 4-6 is all) and union of fracture stage after fixed a period of time, respectively the fracture model is carried out in the different stages limited Meta-analysis, obtain parameter as follows：Axially-movable, shearing motion, compressive stress, contact moment of flexure, mean stress and maximum distortion；According to The different composite blade plate structures are analyzed, are finally selected most beneficial for union of fracture by the result of the parameter Composite blade plate optimum optimization structure.

Claims (5)

1. a kind of composite blade plate Optimization Design based on Laminated Plate Theory, comprises the steps：

Step one：The material for choosing composite blade plate carries out preliminary structure design to which；

Step 2：The structural nature of composite blade plate is laminated plate structure, according to laminate design principle, to composite The structure of blade plate is optimized design；

Step 3：The structure of laminate design principle is unsatisfactory in removing be possible to structure；

Step 4：Theory of the structure based on Analysis of Symmetric Laminated Plates to meeting laminate design principle, with C language in VS2013 platforms Under write code, solve its axial rigidity, bending stiffness and torsional rigidity respectively；

A. the calculating of axial rigidity：

$EA=\frac{b}{A_{11}^{*}}---\left(1\right)$

In formula, axial rigidities of the EA for blade plate, width of the b for blade plate；

B. the calculating of bending stiffness：

${\mathrm{EI}}_{yy}=\frac{b}{D_{11}^{*}}---\left(2\right)$

In formula, EI_yyFor the bending stiffness of blade plate；

C. the calculating of torsional rigidity：

$GJ=\frac{4b}{D_{66}^{*}}---\left(3\right)$

In formula, torsional rigidities of the GJ for blade plate；

Step 5：According to the result of calculation of step 4, structure of the bending stiffness less than setting is removed；

Step 6：Suitable interval is selected according to its bending stiffness to meeting all structures of laminate design principle, is divided For some intervals；

Step 7：The structured stiffness coefficient of institute in each described interval is calculated respectively, and in retaining each interval, stiffness coefficient value is most A kind of high structure；

The computing formula of stiffness coefficient is as follows：

${\mathrm{SEF}}_i=0.5\left(\frac{{\mathrm{EA}}_{min}}{{\mathrm{EA}}_i}\right)+0.5\left(\frac{{\mathrm{GJ}}_i}{{\mathrm{GJ}}_{\max }}\right)---\left(4\right)$

In formula, SEF_iFor the stiffness coefficient of different structure blade plate, EA_minFor the minima of axial rigidity, EA_iConnect for different structure The axial rigidity of hone lamella, GJ_iFor the torsional rigidity of different structure blade plate, GJ_maxFor the maximum of torsional rigidity；

Step 8：The structure of reservation is applied in union of fracture phantom carries out finite element analyses, selects the synthetism of optimum Hardened structure, completes the optimization design of blade plate.

2. the composite blade plate Optimization Design based on Laminated Plate Theory according to claim 1, its feature exist In：In the step one, the composite blade plate cladding material is carbon fiber and/or epoxy resin, and inner layer material is sub- Flaxen fiber and/or epoxy resin.

3. the composite blade plate Optimization Design based on Laminated Plate Theory according to claim 1, its feature exist In：In described step two, the optimization design is carried out rationally to blade plate gross thickness according to actual human body fracture site first Design, then the number according to laminate design principle to laminate laying total quantity, carbon fiber and/or epoxide resin material laying Amount and the quantity of flax fiber and/or epoxide resin material laying, the thickness of laying, laying order and laying direction carry out excellent Change design, the laminate design principle is as follows：

1) balance and symmetry principle of paving：

Composite blade plate structure is designed to into Analysis of Symmetric Laminated Plates form, and laminate laying order must be with regard in laminate Plane symmetry；To avoid in production process due to temperature change and drawing-cut, the buckling deformation that stretching-bending coupling is caused, maximize The bending strength of laminate；

2) laying orientation principle：

Laying direction θ in laminate, is the laying with respect to reference axis for θ ° of direction, and scope is+θ ° and-θ ° of laying from 0 ° to 90 ° Quantity is identical, and the angle between adjacent laying is less than 45 °, and the laying quantitative proportion in any laying direction is less than 60%, with maximum Change the bending strength of laminate；

3) laying minimum scale principle：

To make the matrix of composite stand under load and not avoid thermal coefficient of expansion too high in manufacture process from leading in all directions Buckling deformation is caused, the laying minimum scale in its 0 °, 90 ° laying direction of laminate of laying composition is 10%；

4) open region laying principle：

Angle≤45 ° of adjacent laying should be made in structural openings area, to reduce inter-laminar stress；Opening shape should as far as possible using circle Hole, because circle hole-edge stress concentration is less；In addition in opening, the fiber of cut-out should lack as far as possible；

5) lay principle of temporal sequence：

Mainly from from the aspect of three：Each orientation monolayer should be made to be uniformly distributed along lamination plate thickness as far as possible, it is to avoid by same wing flapping Laying concentrate place；If have to use, 4 layers are usually no more than, to reduce the cracking and edge point of two kinds of oriented layers Layer；If containing ± 45 ° of layers, 0 ° of layer and 90 ° of layers in laminate, should try one's best between+45 ° of layers and -45 ° of layers with 0 ° of layer or 90 ° Layer separates, and is separated with+45 ° of layers or -45 ° of layers, and should avoid laying 90 ° of layers in groups, to reduce layer between 0 ° of layer and 90 ° of layers Between stress；For exposure laminate outside, lay fabric or ± 45 ° of layers on surface, will with preferable working service, Laminate and compression and shock resistance can be improved；In addition, laying order affects very big to laminate stability bearing capacity, This factor should also take into full account；

6) face principle of paving in laminate：

Middle face refers to the plane of symmetry in the middle of Analysis of Symmetric Laminated Plates, and there is the laying that at least 6 laying directions are 90 ° in middle face；In minimum Degree affects to increase its lateral stiffness while bending and torsional rigidity；

7) thickness design principle：

In structure Varying-thickness region, laying number increasing or decreasing should form step and gradually change, because the mutation of thickness can cause Stress concentration；It is required that each step width is close and >=60 °, shoulder height less than width 1/10；Then lay on surface Continuous coating, to prevent from stripping damage outside step.

4. the composite blade plate Optimization Design based on Laminated Plate Theory according to claim 1, its feature exist In：In the step 4, regard blade plate as compound girder construction and process is analyzed based on classical Laminated Plate Theory, axial direction The stiffness matrix derivation of rigidity, bending stiffness and torsional rigidity is as follows：

The power and torque such as formula (5) of laminate unit length, (6) are shown：

$\left[\begin{array}{c}{N}_x\\ N_y\\ N_{xy}\end{array}\right]=\left[\begin{array}{ccc}{A}_{11}& A_{12}& A_{16}\\ A_{12}& A_{22}& A_{26}\\ A_{16}& A_{26}& A_{66}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right]+\left[\begin{array}{ccc}{B}_{11}& B_{12}& B_{16}\\ B_{12}& B_{22}& B_{26}\\ B_{16}& B_{26}& B_{66}\end{array}\right]\left[\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right]---\left(5\right)$

$\left[\begin{array}{c}{M}_x\\ M_y\\ M_{xy}\end{array}\right]=\left[\begin{array}{ccc}{B}_{11}& B_{12}& B_{16}\\ B_{12}& B_{22}& B_{26}\\ B_{16}& B_{26}& B_{66}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right]+\left[\begin{array}{ccc}{D}_{11}& D_{12}& D_{16}\\ D_{12}& D_{22}& D_{26}\\ D_{16}& D_{26}& D_{66}\end{array}\right]\left[\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right]---\left(6\right)$

In formula, A is tensible rigidity matrix, B is Coupling stiffness matrix, D is bending stiffness matrix, because B_ij=0, therefore power and torque Shown in matrix such as formula (7), formula (8)：

$\left[\begin{array}{c}{N}_x\\ N_y\\ N_{xy}\end{array}\right]=\left[\begin{array}{ccc}{A}_{11}& A_{12}& A_{16}\\ A_{12}& A_{22}& A_{26}\\ A_{16}& A_{26}& A_{66}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right]---\left(7\right)$

$\left[\begin{array}{c}{M}_x\\ M_y\\ M_{xy}\end{array}\right]=\left[\begin{array}{ccc}{D}_{11}& D_{12}& D_{16}\\ D_{12}& D_{22}& D_{26}\\ D_{16}& D_{26}& D_{66}\end{array}\right]\left[\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right]---\left(8\right)$

$N_x=\frac{\stackrel{\‾}{N}}{b}---\left(9\right)$

In formula,For the axial force of laminate, width of the b for laminate, using Laminated Plate Theory, N_xIt is long for unit in laminate Shown in the power of degree, such as formula (9)；

It is assumed that N_xFor (the namely N in formula (7) of unique power in laminate_y=N_xy=0), formula (7) is changed into：

$\left[\begin{array}{c}{\mathrm{\ϵ}}_x^0\\ {\mathrm{\ϵ}}_y^0\\ {\mathrm{\γ}}_{xy}^0\end{array}\right]={\[A\]}^{-1}\left[\begin{array}{c}{N}_x\\ 0\\ 0\end{array}\right]---\left(10\right)$

${\mathrm{\ϵ}}_x^0=A_{11}^{*}{N}_x---\left(11\right)$

In formula, $A_{ij}^{*}$ For matrix [A]^-1In element,For the strain on x-axis direction；

${\mathrm{\ϵ}}_x^0=\frac{\∂u_0}{\∂x}---\left(12\right)$

In formula, u₀For the displacement on x-axis direction, in narrower girder construction, when length-width ratio is sufficiently high, it can be assumed that u₀= u₀(x), therefore formula (12) can be equal to formula (13)：

${\mathrm{\ϵ}}_x^0=\frac{{\mathrm{du}}_0}{dx}=A_{11}^{*}{N}_x---\left(13\right)$

$\frac{du}{dx}=\frac{N}{EA}---\left(14\right)$

The axial direction of anisotropy Symmetric Beam is obtained according to the axial strain (i.e. formula (14)) of formula (13) and isotropism beam Shown in the computing formula of rigidity such as formula (15)：

$EA=\frac{b}{A_{11}^{*}}---\left(15\right)$

In order to be bent rigidity EI_yy, a Based on Pure Bending Moment (M_y) act on X-Z plane, the torque of unit lengthCalculate public Shown in formula such as formula (16)：

$M_x=\frac{\stackrel{\‾}{M_y}}{b}---\left(16\right)$

$\left[\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right]={\[D\]}^{-1}\left[\begin{array}{c}{M}_x\\ 0\\ 0\end{array}\right]---\left(17\right)$

$K_x=D_{11}^{*}{M}_x---\left(18\right)$

In formula,For matrix [D]^-1In element；

The computing formula such as formula (19) of the planar curvature outside the planar curvature of X-Z plane and middle face, (20) are shown：

$K_x=-\frac{{\∂}_{w0}^2}{\∂x^2}---\left(19\right)$

$K_{xy}=-2\frac{{\∂}_{w0}^2}{\∂x\∂y}---\left(20\right)$

In formula, w0 is the displacement on combination beam z-axis direction, because beam is narrower, here it is assumed that w0=w0 (x), formula (19) equivalent In formula (21)；

$K_x=-\frac{d_{w0}^2}{{\mathrm{dx}}^2}=D_{11}^{*}{M}_x---\left(21\right)$

According to formula (21) and the curvature (d of isotropic rectangle beam²w/dx²=-(M/EI)), then anisotropy rectangular beam is curved Shown in stiffness such as formula (22)：

${\mathrm{EI}}_{yy}=\frac{b}{D_{11}^{*}}---\left(22\right)$

To obtain the torsional rigidity of composite blade plate square-section, it is assumed that any torque T being applied on beam can produce list Bit length moment of torsion (M_xy) and subsequent shear flow (q), shown in the shear flow that torque T causes such as formula (23)：

T=2qh ' b ' (23)

In formula, h ' is the thickness of laminate after shear flow effect, and b ' is the width of laminate after shear flow effect；

The moment of torsion of square-section unit length is：

M_xy=-qh ' (24)

Can be obtained by formula (23), (24)：

T=-2bM_xy (25)

By formula (8), it is contemplated that actually there is no curvature K of axial force and Moment on beam, in laminate outside face_xyFor：

$\left[\begin{array}{c}{K}_x\\ K_y\\ K_{xy}\end{array}\right]={\[D\]}^{-1}\left[\begin{array}{c}0\\ 0\\ M_{xy}\end{array}\right]---\left(26\right)$

$K_{xy}=D_{66}^{*}{M}_{xy}---\left(27\right)$

Shown in the torsion ψ and torsion curvature ξ such as formula (28), (29) of beam middle section：

$\mathrm{\ψ}=\frac{\∂w_0}{\∂y}---\left(28\right)$

$\mathrm{\ξ}=\frac{\∂\mathrm{\ψ}}{\∂x}---\left(29\right)$

Curvature outside face in composite beam can be expressed as by formula (20) and (28)：

$K_{xy}=-2\frac{\∂(\∂w_0/\∂y)}{\∂x}=-2\frac{\∂\mathrm{\ψ}}{\∂x}---\left(30\right)$

Therefore can obtain：

$\mathrm{\ξ}=-\frac{1}{2}{K}_{xy}---\left(31\right)$

By formula (25), (27), (31), torsion curvature such as formula (32) institute of the rectangle composite beam in the torque for being applied can be obtained Show：

$\mathrm{\ξ}=\frac{D_{66}^{*}}{4b}T---\left(32\right)$

ξ=T/GJ (33)

$GJ=\frac{4b}{D_{66}^{*}}---\left(34\right)$

According to the computing formula (33) of formula (32) and the torsion curvature of isotropism beam, with square-section and sufficiently high width Thickness rate is shown in the torsional rigidity such as formula (34) of symmetrical composite beam.

5. the composite blade plate Optimization Design based on Laminated Plate Theory according to claim 1, its feature exist In：In the step 8, the blade plate structure of reservation is applied in the union of fracture analogue system of C language written in code, is entered Row finite element analyses, take into full account the actual therapeutic scheme of patient, simulate different gait load, and will use when writing code It is (i.e. just solid using blade plate that the fracture healing process of the fracture model after composite plate fixation is divided into Post operation immediately Regularly), (about 4-6 is all) and union of fracture stage after fixed a period of time, in the different stages respectively to the fracture model Finite element analyses are carried out, parameter is obtained as follows：Axially-movable, shearing motion, compressive stress, contact moment of flexure, mean stress and maximum Deformation；According to the result of the parameter, the different composite blade plate structures are analyzed, finally select most beneficial for The optimum optimization structure of the composite blade plate of union of fracture.