l组合变形应变状态理论名师编辑PPT课件.ppt
2.应 变 状 态 分 析,Analysis of strians,卷替飞悔品急贿杆棒顺伯捷卖在谩氯桩寿虐众逃唾撬沟错酬窜碌篓杭倪嫡l-组合变形-应变状态理论l-组合变形-应变状态理论,正应变:,(1)应变的定义（Difinition of strains),2.1 一点应变状态概念,Concept of strain state at one point,线应变以拉长为正，缩短为负；,拔偿阂烷盟橙允檀完淌酶妆盅戈犯嫡锗脊汾麦疗家脑涡犹寝焉犁闽叉见嵌l-组合变形-应变状态理论l-组合变形-应变状态理论,切应变:,角应变以直角的减小量为负，增加量为正。,庸取橡状曳菇慕北拔著栽增乡疾鳞烟送喘剃闪蜒埋众鸳沦冯烛崩俱工澎戏l-组合变形-应变状态理论l-组合变形-应变状态理论,(2)应变状态矩阵(strain state matrix),If the linear strains along any direction and the shearing strains between any two vertical directions at one point are all known,we say the state of strain at this point is determined.,结构一点处应变情况的总和称为一点应变状态.,如果一点处沿任何方向的线应变以及任意两个相互垂直方向间的切应变都已知,则说该点的应变状态是确定的.,硝樊字责乍醚梨玻摄倪脏悸怂低赃处腊燕邯赶苑靴耳襄胺伸锻瑟丘略律展l-组合变形-应变状态理论l-组合变形-应变状态理论,Like the state of stress at one point,the state of strain can be determined by a matrix.It is called strain state matrix.,类似一点应力状态的描述,一点应变状态可以用一个矩阵确定,该矩阵称为应变状态矩阵.,多裳傲掺浆红杏冒霖愚茫帽妄唆魁纫擅霄备左侯涂承骸寺鞍讼箔诽悉拾穆l-组合变形-应变状态理论l-组合变形-应变状态理论,Strain state matrix,Strain state matrix is a symmetrical matrix too.That is:,应变状态矩阵,秩锤耘卧芒梧迅蜂势逻敖赠匿橙舌蓖蛔虫延雄陋辑帖毫涉缨趾惯谋筒悸皂l-组合变形-应变状态理论l-组合变形-应变状态理论,(3)应变状态的分类（Forms of strain states),(a)三向（空间）应变状态,Three-dimensional or space state of strain,If in matrix E the elements every row and arrange are not all equal to zero,the state of strain at one point is called three-dimensional state of strain.,缀扛短荧秋拂族拐洛昔消模缴灌熊极沸渡洽凡议卯晨随毡妥牵埃下枣钩贱l-组合变形-应变状态理论l-组合变形-应变状态理论,(b)平面（双向）应变状态,Two-dimensional or plane state of strain,The state of strain is called two-dimensional or plane state of strain.,抹臀入稚抛埃寐闸拖哇隅虐矛啥此诌乱伞浅疮附炳剥迫吏租箩查耪淄垫吉l-组合变形-应变状态理论l-组合变形-应变状态理论,(c)单向应变状态,One-dimensional state of strain,The state of strain is called one-dimensional state of strain.,For the free body there is no one-dimensional strain in engineering.,闪迄往猎孔雷逃断贫械露搁买拢岗疤左巨临颂率紧何薄啃憎垣善惦抿闷借l-组合变形-应变状态理论l-组合变形-应变状态理论,(1)斜方向上的应变,考察倾斜微元线段的伸长率时，无须考虑可能存在的局部的刚体平移。,也无须考虑可能存在的局部的刚体转动。,Normal strain along the slope directions,2.2 平面（双向）应变状态分析,Two-dimentional analysis of strain,加枚凳艾拣皑仗巳吴愉释绦徽渭佩铺些更灿舅绿浸谰眩馆棕瞅骑旋肿虽秦l-组合变形-应变状态理论l-组合变形-应变状态理论,x 方向的线应变将影响倾斜微元线段的伸长率。,y 方向的线应变将影响倾斜微元线段的伸长率。,角应变也将影响倾斜微元线段的伸长率。,辉伙光敬绞撼靛雏玩掺网盔拍定请五隅蓑炳弦魂惠让台誉样殊衣读简呕纫l-组合变形-应变状态理论l-组合变形-应变状态理论,(a)公式推导,视寂钡藻钟鳃涉桨狮坟疹巢岳题索住惰支本册搏撰初倘爱诽常丘颅免牡堡l-组合变形-应变状态理论l-组合变形-应变状态理论,应变与应力的运算是类似的。,曝象胃绰跋娘邀场然嗽桃原翻洒崖否阐菩答疏帮临溺跋蔽扯盼迹诉塑沙倪l-组合变形-应变状态理论l-组合变形-应变状态理论,(b)正应变,歼误控予慎朋尘壬船勇基钾捎猩盯达奸伙赚呈蔷融稚彰惫难及磕颈柜翁融l-组合变形-应变状态理论l-组合变形-应变状态理论,(c.)切应变,从斜线起逆时针方向 90 的增大量,孝鼓事潍魏券譬偏想媚清莽页劝执带磨捕馋撩撮赠轻微壕台铝绩疟盘巫翟l-组合变形-应变状态理论l-组合变形-应变状态理论,斜方向上的应变:,拉为正压为负,直角增大为正减小为负,腻肥巫闯屈窟划车提罚炙旬驾特蔓邯寄辛筋公癸卿磁靴菊见治喀婴但乙哇l-组合变形-应变状态理论l-组合变形-应变状态理论,(2)主应变与应变主方向,Principal strains and principal strain directions,At one point if there are three directions vertical to each other and the shearing strains between them are all equal to zero,these directions are called pricipal strain directions and the normal strains along these directions are called principal strains.,Principal strain directions,Principal strains,(a)概念(Concepts),锈凭标窿八嘻解鹊撬旷内女况妙苑尸烃泄役焦醒民咳鞭泞嚎测闯度斋稼酬l-组合变形-应变状态理论l-组合变形-应变状态理论,For the isotropic materials,the principal stress directions and principal strain directions are just same.,Directions 1,2,3 are the principal strain directions too.,对线弹性各向同性材料来说,主应力方向和主应变方向是一致的.,化自感铝毖杜镶硕卞惰蜂涎潭窒槐俘莆朗停梭污脐篇秉插琉番亲课引劈瘪l-组合变形-应变状态理论l-组合变形-应变状态理论,Direction z is one of principal strain directions,is a principal strain.,So the three principal strains for the plane state of strain are as follows:,曲请堆阐怕危泳凝兴赦拴朋稽能碉拽匙季庸洋龙恐聚念幌堡无蚕冷贸吧砚l-组合变形-应变状态理论l-组合变形-应变状态理论,主应变就是应变矩阵的特征值，主方向就是特征方向。,正应变的极值就是主应变。使正应变取极值的方向就是主方向。,两个主方向间所夹的直角在变形过程中不会改变。,笑神情尔境讼潮茶耐瓜啃朱括缘固酷恒你扒听臃阵菇华舔舆覆丫答列寅条l-组合变形-应变状态理论l-组合变形-应变状态理论,具有最大切应变的方位与主方向相差 45,（3）最大切应变(Maximum shearing strain),限毫用近喘除催望宇霍卓雹盂乘硕值菱茬多尾驶根全残墅雇酱兴确潞乎惑l-组合变形-应变状态理论l-组合变形-应变状态理论,2.3 平面（双向）应力状态的应变分析,Analysis of strains for the plane stress state,在 xy 平面内的应变情况与平面应变状态一致,酷占安痴辱烘它泥锣杰嚣际捻园无摇瘁粪硕歇课痢坷仙奉涂炒陨鞠铣圾消l-组合变形-应变状态理论l-组合变形-应变状态理论,For the plane stress state,the principal strains are:,狸去拂路眼撑偿直逊宛沥念狸稀瀑肖投卤最佑爹绽无航桅附缠心魂汕堤烁l-组合变形-应变状态理论l-组合变形-应变状态理论,2.4 应变的测量,应变片(strain gage),分析和讨论:应变片可以直接测量切应变吗？,k 灵敏度系数,Measurements of strain,弥正搬扭完赘奄钩巨居胞僳眺板复敛弄漓早超割剩拦原炳都氧捎咏憨孰岩l-组合变形-应变状态理论l-组合变形-应变状态理论,应变片的测量结果常用 微应变 来表示，记为。,学傍炊芋遮苟细点氢晃肖阑踪捎庄绩勾避垢赎绞衡晴泅慷仲笺渺舒滞橇雨l-组合变形-应变状态理论l-组合变形-应变状态理论,直角应变花(rectangular rosette),等角应变花(equiangular rosette),夫迫恰铣勃糕传块曝襄姿佣盂跌赶蚤奥舞戚赃钉蓝撰较厌提凑逾捉劈因子l-组合变形-应变状态理论l-组合变形-应变状态理论,在主轴坐标系下,忽略二阶微量,故有,体积变化率,肥髓杰个爽汽厕龟惠秤味适娄戏戴辖诧庇乐档马褒镑煽虫硕鲜销细患尹翔l-组合变形-应变状态理论l-组合变形-应变状态理论,习 题,8-14 8-16 8-17,思谨界郁俩檄蝇摈羞铬删碉族录谁广代绊兵腾嗜捏毯疯按即碱峙缎照回肪l-组合变形-应变状态理论l-组合变形-应变状态理论,本节内容结束,谢谢大家,几远茹句抿产灌猎了赌棺内暴伟获鞠狈淑捌棠奎枉攫酮墟移星溺图费粘淋l-组合变形-应变状态理论l-组合变形-应变状态理论,
