横向均布载荷下预应力圆薄膜最大挠度的确定方法

专利类型：发明专利

语言：中文

申请号：CN201610802706.9

申请日：20160905

发明人：孙俊贻杨志欣练永盛李珂郭莹郑周练何晓婷

申请人：重庆大学

申请人地址：400044 重庆市沙坪坝区沙正街174号

公开日：20161221

公开号：CN106248474A

代理人：黄河

代理机构：重庆博凯知识产权代理有限公司 50212

摘　　要：本发明公开了横向均布载荷下预应力圆薄膜最大挠度的确定方法：对周边固定夹紧的预应力圆形薄膜横向施加一个均布载荷q，其中圆形薄膜的厚度为h、半径为a、杨氏弹性模量为E、泊松比为ν、预应力为σ₀，基于这个轴对称变形问题的静力平衡分析，利用均布载荷q的测量值，则可以确定出薄膜变形后的最大挠度w_m。

主权项：横向均布载荷下预应力圆薄膜最大挠度的确定方法，其特征在于：对周边固定夹紧的预应力圆形薄膜横向施加一个均布载荷q，其中圆形薄膜的厚度为h、半径为a、杨氏弹性模量为E、泊松比为ν、预应力为σ₀，测得所施加的均布载荷q的值，由以下公式确定该圆形薄膜变形后的最大挠度w_m： $\begin{matrix} w_{m} = {(\frac{a^{2} q c}{2 h E})}^{1 / 3} [1 + (\frac{1}{4} + \frac{1}{2} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}}) c + (\frac{5}{36} + \frac{11}{18} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + \frac{1}{2} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}}) c^{2} \\ + (\frac{55}{576} + \frac{49}{72} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + \frac{61}{48} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + \frac{5}{8} \frac{2 a^{2} q^{2}}{h^{2} E^{c} c}) c^{3} + (\frac{7}{96} + \frac{2647}{3600} \frac{2^{1 / 2} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + \frac{4051}{1800} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + \frac{253}{100} \frac{2 a^{2} q^{2}}{h^{2} E^{2} c} + \frac{7}{8} \frac{2^{4 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}}) c^{4} + (\frac{205}{3456} + \frac{101639}{129600} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + \frac{443119}{129600} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + \frac{8521}{1350} \frac{2 a^{2} q^{2}}{h^{2} E^{2} c} + \frac{7141}{1440} \frac{2^{4 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} + \frac{21}{16} \frac{2^{5 / 3} a^{10 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}}) c^{5} \\ + (\frac{17051}{338688} + \frac{2639243}{3175200} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + \frac{866077}{181440} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + \frac{13308283}{1058400} \frac{2 a^{2} q^{2}}{h^{2} E^{2} c} \\ + \frac{1904549}{117600} \frac{2^{4 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} + \frac{113623}{11760} \frac{2^{5 / 3} a^{10 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}} + \frac{33}{16} \frac{4 a^{4} q^{4}}{h^{4} E^{4} c^{2}}) c^{6} + (\frac{2864485}{65028096} \\ + \frac{5947093}{6773760} \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + \frac{91705651}{14515200} \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + \frac{1115512751}{50803200} \frac{2 a^{2} q^{2}}{h^{2} E^{2} c} \\ + \frac{1366411591}{33868800} \frac{2^{4 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} + \frac{740195}{18816} \frac{2^{5 / 3} a^{4 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}} + \frac{33661}{1792} \frac{4 a^{4} q^{4}}{h^{4} E^{4} c^{2}} \\ + \frac{429}{128} \frac{2^{7 / 3} a^{14 / 3} q^{14 / 3}}{h^{14 / 3} E^{14 / 3} c^{7 / 3}}) c^{7}] \end{matrix},$ 而中间参量c的值由方程 $[2 {cf}^{'} (c) + (1 - v) f (c)] - (1 - v) \frac{2^{5 / 3} h^{2 / 3} c^{1 / 3}}{a^{2 / 3} q^{2 / 3} E^{1 / 3}} σ_{0} = 0$ 确定，其中， $\begin{matrix} f (c) = 1 - \frac{1}{2} c - \frac{1}{6} (1 + 2 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}}) c^{2} - \frac{1}{144} (13 + 56 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 48 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}}) c^{3} - \frac{1}{1440} (85 + 584 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + 1104 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} \\ + 1152 \frac{a^{2} q^{2}}{h^{2} E^{2} c}) c^{4} - \frac{1}{21600} (925 + 8904 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + 27104 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} \\ + 62592 \frac{a^{2} q^{2}}{h^{2} E^{2} c} + 23040 \times \frac{2^{1 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}}) c^{5} - \frac{1}{907200} (30125 + 377688 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 1619968 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + 6038784 \frac{a^{2} q^{2}}{h^{2} E^{2} c} + 4907520 \times \frac{2^{1 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} \\ + 1382400 \times \frac{2^{2 / 3} a^{10 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}}) c^{6} - \frac{1}{203212800} (5481025 + 85400640 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 478992416 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + 2520947712 \frac{a^{2} q^{2}}{h^{2} E^{2} c} + 3305599488 \times \frac{2^{1 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} \\ + 2047057920 \times \frac{2^{2 / 3} a^{10 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}} + 928972800 \frac{a^{4} q^{4}}{h^{4} E^{4} c^{2}}) c^{7} \end{matrix},$ $\begin{matrix} f^{'} (c) = - \frac{1}{2} - \frac{1}{3} (1 + 2 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}}) c - \frac{1}{48} (13 + 56 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 48 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}}) c^{2} - \frac{1}{360} (85 + 584 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + 1104 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} \\ + 1152 \frac{a^{2} q^{2}}{h^{2} E^{2} c}) c^{3} - \frac{1}{4320} (925 + 8904 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} + 27104 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} \\ + 62592 \frac{a^{2} q^{2}}{h^{2} E^{2} c} + 23040 \times \frac{2^{1 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}}) c^{4} - \frac{1}{151200} (30125 + 377688 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 1619968 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h^{4 / 3} E^{4 / 3} c^{2 / 3}} + 6038784 \frac{a^{4} q^{2}}{h^{2} E^{2} c} + 4907520 \times \frac{2^{1 / 3} a^{8 / 3} q^{8 / 3}}{h^{8 / 3} E^{8 / 3} c^{4 / 3}} \\ + 1382400 \times \frac{2^{2 / 3} a^{10 / 3} q^{10 / 3}}{h^{10 / 3} E^{10 / 3} c^{5 / 3}}) c^{5} - \frac{1}{29030400} (5481025 + 85400640 \times \frac{2^{1 / 3} a^{2 / 3} q^{2 / 3}}{h^{2 / 3} E^{2 / 3} c^{1 / 3}} \\ + 478992416 \times \frac{2^{2 / 3} a^{4 / 3} q^{4 / 3}}{h关键词：法律状态：生效IPC专利分类号： G01N3/00(2006.01)Ivar ShareData = new Array();
$(function () {
$('#btnShare').mouseover(function () {
ShareData = {};
var title = $(this).attr('btitle');
ShareData['url'] = location.href;
ShareData['title'] = title;
});

$("#btnDown").click(function () {
message("全文下载中......");
$.ajax({ url: "/ajax/log.ashx?type=down&id=" + $(this).attr("lngid"), async: false });
location.href = $(this).attr("url");
});

//评论
$('#txtcontent').xheditor({ tools: "Fontface,FontSize,Bold,Italic,Underline,Align,List,OutdentIndent,Link,Img,Emot", upImgUrl: "/ajax/XheditorUpload.ashx?isajax=1&isformsubmit=1", upImgExt: "jpg,jpeg,gif,png" });

//评论显示
$.ajax({
type: "post",
url: "/ajax/CommentPaper.ashx?t=" + Math.random(),
data: { "action": "show", "lngid": "c1dffda768a32789" },
dataType: "json",
beforeSend: function () {
$("#commentlist").html("正在加载...");
},
success: function (data) {
var result = data.result || 0;
var message = data.message || "操作失败";
if (result > 0) {
$("#commentlist").html(data.html);
} else {
alert(message);
}
}
});

//设置打分效果
$("#star").raty({
hints: ['2', '4', '6', '8', '10'],//鼠标移上图片显示的文字
path: "/images",
target: '#hidscore',//设置选中时候赋值
targetKeep: true,//targetKeep 属性设置为true，用户的选择值才会被保持在目标hidscore中，否则只是鼠标悬停时有值，而鼠标离开后这个值就会消失
size: 24
});

});
function SetShareData(cmd, config) {
config.bdUrl = ShareData['url'];
config.bdText = ShareData['title'];

return config;
}

function removeHTMLTag(str) {
//str = str.replace(/<\/?[^>]*>/g, ''); //去除HTML tag
str = str.replace(/[ | ]*\n/g, '\n'); //去除行尾空白
str = str.replace(/\n[\s| | ]*\r/g,'\n'); //去除多余空行
//str = str.replace(/ /ig, '');//去掉
str = str.replace(/(<br\s?\/?>)+/gi, '$1');//去出重复的<br/>
return str;
}

//评论
function setComment() {
var verifycode = $("#verifycode").val();
var content = $("#txtcontent").val();
var score = $("#hidscore").val();
var userName = $("#txtUserName").val();
var newcontent = removeHTMLTag(content);
newcontent = newcontent.replace(/ /ig, "");
if (verifycode.length <= 0) {
alert("请输入验证码！");
} else if (newcontent.length < 1) {
alert("评论内容不能为空！");
} else if (score == "") {
alert("评分不能为空");
} else {
$.ajax({
type: "post",
url: "/ajax/CommentPaper.ashx?t=" + new Date(),
data: { "action": "comment", lngid: "c1dffda768a32789", title: "", comtent: newcontent, grade: score, userName: userName,verifycode:verifycode },
dataType: "json",
success: function (data) {
var result = data.result || 0;
var message = data.message || "操作失败";
if (result > 0) {
alert(message, location.href);
} else if (result == -1) {
alert(message, "/login.aspx");
} else {
message(message);
}
}
});
}

}

function goPage(obj) {
$.ajax({
type: "get",
url: "/ajax/CommentPaper.ashx",
data: { "action": "show", "pagesize": 5, "lngid": "c1dffda768a32789", "page": obj },
dataType: "json",
success: function (result) {
$("#commentlist").html(result.html);
}
});
}
/**刷新验证码*/
function refreshImg() {
var timenow = new Date().getTime();
document.getElementById('secimg').src = "/ajax/getauthcode.ashx?" + timenow;
document.getElementById('verifycode').value = "";
}
window._bd_share_config = { "common": { onBeforeClick: SetShareData, "bdText": "", "bdMini": "2", "bdMiniList": false, "bdPic": "", "bdStyle": "1", "bdSize": "20" }, "share": {} }; with (document) 0[(getElementsByTagName('head')[0] || body).appendChild(createElement('script')).src = 'http://bdimg.share.baidu.com/static/api/js/share.js?v=89860593.js'];Copyright © 2018 版权所有：重庆大学知识产权信息服务中心总机:023-65106364 技术支持：重庆维普资讯有限公司var request = g_getUrlParms();
$(function () {
var encodestr = decodeURI($("#hifBaseLog").val().trim()).toString();
var BaseGch = "";
var BaseArticleId = "";
var BaseClass = "";
var BaseObjectType = 0;
var BaseObjectValue = "";
var PageUrl = "";
var ReferrerUrl = "";

if (encodestr != "") {
var parames = encodestr.split(';');
BaseGch = parames[0];
BaseArticleId = parames[1];
BaseClass = parames[2];
BaseObjectType = parames[3];
BaseObjectValue = parames[4];
PageUrl = parames[5];
ReferrerUrl = parames[6];
}

var obj = {};
obj.remark = "机构库站点访问记录-重庆大学";
obj.user_id = "0";
obj.user_ip_address = "18.118.164.100";
obj.user_group_id = "0";
obj.user_organ_id = "0";
obj.site_id = 13;
if (BaseGch) {
obj.gch = BaseGch;
}
if (BaseArticleId) {
obj.article_id = BaseArticleId;
}
if (BaseClass) {
obj.full_class_ids = BaseClass;
}
if (BaseObjectType) {
obj.object_id = BaseObjectType;
}
if (BaseObjectValue) {
obj.object_value = BaseObjectValue;
}
if (PageUrl) {
obj.pageurl = PageUrl;
}
if (ReferrerUrl) {
obj.referrerurl = ReferrerUrl;
}

vipLog("view", obj);

//返回顶部开始
$('#backtop').hover(function () {
$(this).css({ opacity: 1 });
},
function () {
$(this).css({ opacity: 0.8 });
});

$('#backtop').click(function () {
$('html,body').animate({ scrollTop: 0 }, 100);
});

$(window).scroll(function () {
var scroH = document.documentElement.scrollTop + document.body.scrollTop;
if (scroH > 100) {
$('#backtop').show();
} else {
$('#backtop').hide();
}
});
//返回顶部结束
});
//页面加载完成后事件
jQuery().ready(function () {
navigation();
});
function vipLog(type, obj) {
$.post("/ajax/log.ashx", { type: type, obj: JSON.stringify(obj) });
}
//面包屑导航
function navigation() {
var title = $(".nav-list").find(".nav_hover a").eq(0).text();
var childurl = "";
var childtitle = $(".nav-list").find(".nav_hover a[class='select_hover']").text();
var html = "<a href=\"javascript:void(0);\">" + title + "</a>";
if (childtitle != title) {
if (childtitle != "" && childtitle != undefined) {
html = "<a class=\"current\" href=\"javascript:void(0);\">" + title + "</a>";
html += "> <a href=\"javascript:void(0);\">" + childtitle + "</a>";
}
}
$("#navigation").html(html);
}} \end{matrix}$